Law of Julianos - Availability: Crafted- Difficulty to acquire: Trivial
(2 items) Adds 833 Spell Critical
(3 items) Adds 1096 Maximum Magicka
(4 items) Adds 833 Spell Critical
(5 items) Adds 299 Spell Damage.

Crafted in Wrothgarr once your character knows 6 equipment traits --- or have someone make it for you!
Considered by many to be a staple of magicka sets. It provides solid, permanent stat bonuses with no particular requirements on playstyle. It also serves as a good benchmark; if your magicka set performs worse than Julianos on average, it's probably bad.
Ask a nice guild member to make you a set! It's a great starting point.

Mother's Sorrow - Availability: Deshaan Overland or Guildstores - Difficulty to acquire: Varies
(2 items) Adds 1096 Maximum Magicka
(3 items) Adds 657 Spell Critical
(4 items) Adds 657 Spell Critical
(5 items) Adds 1528 Spell Critical

Has essentially been a top tier DPS set since One Tamriel. It provides a positively massive boost to critical strike chance, and will frankly last you through any content in the game.
The strengh of the set is, however, sadly reflected in its price. Inferno staves typically go for no less than 60,000 gold, and often more. If you're a particularly lucky individual or posses supernatural mental fortitude, you might consider farming it yourself in Deshaan.

Burning Spellweave - Availability: City of Ash I or II - Difficulty to acquire: Easy-Medium
(2 items) Adds 1096 Max Magicka
(3 items) Adds 129 Spell Damage
(4 items) Adds 833 Spell Critical
(5 items) When you deal damage with a Flame Damage ability, you apply the burning status effect to the enemy and increase your Spell Damage by 490 for 8 seconds. This effect can occur once every 12 seconds.

While City of Ash II is one of the more difficult classic dungeons, this set can be farmed equally well (read: much more easily) in City of Ash I, and you needn't even make it veteran difficulty.
Note of course that the set only procs from FLAME damage; so you should want to use Inferno Staves with this... You would, any way.
Can be frontbar'd, as the buff is fairly lengthy --- assuming that you're one of those Fortune-kissed people who actually ever find an Inferno staff in the set you want.

Mechanical Acuity - Availability: Crafted - Difficulty to acquire: Trivial
(2 items) Adds 1096 Maximum Stamina
(3 items) Adds 1096 Maximum Magicka
(4 items) Adds 129 Weapon Damage and Spell Damage
(5 items) When you deal direct damage, you gain unerring mechanical vision for 5 seconds, granting you 100% Critical Strike chance. This effect can occur once every 21 seconds.

Crafted in Clockwork City by a Player with 6 researched traits.
This set has seen a lot of changes over the years. Changing between absolutely busted, to nerfed, to okay, to pretty good. It's currently pretty good. Getting 100% critical strike chance on a roughly 20% uptime comes out to... roughly 20% critical strike chance over all. Note that it works equally well for stamina or magicka setups.
Can be frontbar'd, which actually allows you a lot of control over WHEN the acuity procs. This means that you can time it for landing your most devastating strikes, such as ultimate abilities.

Medusa- Availability: Arx Corinium - Difficulty to acquire: Easy
(2 items) Adds 657 Spell Critical
(3 items) Adds 657 Spell Critical
(4 items) Adds 657 Spell Critical
(5 items) Adds 892 Spell Critical, Gain Minor Force at all times, increasing your Critical Damage by 10%.

Farmed in a relatively easy dungeon on veteran or normal difficulty. It grants the important Minor Force buff which, while it is generally available to all builds, can save you some rotation/bar-space ease.
Note that this is a heavy armor set, meaning that you must use it on jewelry/weapon slots, if you want to benefit fully from light armor passives. The jewelry must also be transmuted to provide bonus magicka, instead of additional healthy.

Willpower - Availability: Imperial City, Daily Random Dungeon Rewards or Guild Stores - Difficulty to acquire: Varies
(2 items) Adds 1752 Maximum Magicka
(3 items) Adds 206 Spell Damage

This is the set you use, when you can't fit another full (5)-piece set into your build. Note that they are only available as jewelry or weapons.
They're no longer the most expensive items in the game, and should be purchasable for reasonable prices, if you don't care to enter Imperial City yourself.

Elemental Succession - Availability: Maelstrom Arena - Difficulty to acquire: Medium]
(2 items) Adds 1096 Max Magicka
(3 items) Adds 129 Spell Damage
(4 items) Adds 1096 Max Magicka
(5 items) Whenever you deal Flame, Shock, or Frost Damage, you gain 492 Spell Damage for that element for 4 seconds. This effect can occur every 4 seconds per element. You can have multiple different elemental buffs active simultaneously.

DLC required!
This used to be a sort of gimmicky set, but is actually decent by now. Don't feel that you miss out if you don't proc all 3 effects; just getting 492 fire damage can be immense.
Note that if you use Force Shock destruction staff ability, you can proc all three effects simultaneously. Not reccomended for Nightblades or Templars, as they rely quite a bit on Magic damage, rather than elementals.
Maelstrom Arena isn't exactly easy, but the set can be farmed on normal difficulty and its a fun solo challenge.

Scathing Mage - Availability: Imperial City Prison - Difficulty to acquire: Medium-Hard
(2 items) Adds 1096 Max Magicka
(3 items) Adds 833 Spell Critical
(4 items) Adds 833 Spell Critical
(5 items) When you deal direct Critical Damage, you have a 20% chance to increase your Spell Damage by 516 for 5 seconds. This effect can occur once every 5 seconds.

DLC required!
I'm sort of stretching the "beginner" aspect here, as Imperial City Prison is definitely a tougher dungeon. But it can be farmed on normal mode, so with a good trio of other players you might be fine.

Silks of the Sun - Availability: Stonefalls - Difficulty to acquire: Varies
(2 items) Adds 833 Spell Critical
(3 items) Adds 1096 Max Magicka
(4 items) Adds 129 Spell Damage
(5 items) Adds 400 Spell Damage to your Flame Damage abilities.

Available as random drops, guild stores or even quest rewards in Stonefalls.
Magicka Dragonknights only!. Since your everything is fire as a 'MagDK', the 400 spell damage is really solid.

Elfbane - Availability: Cyrodiil vendors or Guild Stores - Difficulty to acquire: Varies
(2 items) Adds 1096 Maximum Magicka
(3 items) Adds 129 Spell Damage
(4 items) Adds 129 Spell Damage
(5 items) While in combat, increases the duration of your Flame Damage over Time abilities by 5 seconds. This effect does not work with beam or channeled effects.

Purchased with Alliance Points from the Vlastarus Elite Gear Vendor in Cyrodiil. Or from guildstores...
Lo and behold! another set seemingly tailored to Magicka Dragonknights. +5 seconds duration on your Engulfing Flames, Burning Embers, and Cinderstorm translates into better sustain and more time spent spamming Molten Whip!
Note that this is a heavy armor set, meaning that you must use it on jewelry/weapon slots, if you want to benefit fully from light armor passives. The jewelry must also be transmuted to provide bonus magicka, instead of additional healthy.

Spell Strategist - Availability: PVP rewards or Guild Stores - Difficulty to acquire: Varies
(2 items) Adds 1096 Max Magicka
(3 items) Adds 129 Spell Damage
(4 items) Adds 129 Spell Damage
(5 items) When you deal damage with a Light Attack, you place a mark over your target for 5 seconds, granting you 460 Spell Damage against your marked target. This effect can occur every 4 seconds.

Solid single-target damage boost with an easy 100% uptime. If you enjoy PVP you can get it with random "Rewards for the Worthy", or else buy it off guild stores. Can be frontbar'd, since the buff lasts a decent amount of time.

War Maiden - Availability: Vvardenfell or Guild Stores - Difficulty to acquire: Varies
(2 items) Adds 833 Spell Critical
(3 items) Adds 1096 Max Magicka
(4 items) Adds 129 Spell Damage
(5 items) Adds 600 Spell Damage to your Magic Damage abilities

DLC required! Unless purchased
Overland set from Vvardenfell. Decently priced.
Should only be considered on Templar or Nightblades, as other classes rely too heavily on elemental damages (shock, fire, ice) in addition to Magic.

Innate Axiom - Availability: Crafted- Difficulty to acquire: Trivial
(2 items) Adds 129 Weapon and Spell Damage
(3 items) Adds 1096 Maximum Stamina and Max Magicka
(4 items) Adds 833 Critical Chance
(5 items) Adds 400 Spell and Weapon Damage to your Class abilities.

Crafted in Clockwork City by a Player with 2 researched traits.
My heart says yes but my mind says no. It suffers the same issues as the War Maiden's set, since it will do NOTHING to help important destruction staff abilities like Wall of Elements or Elemental rage.

New Moon Acolyte - Availability: Crafted - Difficulty to acquire: Trivial
(2 items) 833 Critical Chance
(3 items) 129 Weapon and Spell Damage
(4 items) 1487 Physical and Spell Penetration
(5 items) Adds 401 Weapon and Spell Damage. Increase the cost of your active abilities by 5%.

Crafted in Southern Elsweyr by a Player with 9 researched traits.
If you can sustain through the extra costs, it's a massive bonus. Note that it works for either Magicka and Stamina.

Diamond's Victory - Availability: Crafted - Difficulty to acquire: Trivial
(2 items) Adds 129 Weapon and Spell Damage
(3 items) Adds 657 Critical Chance
(4 items) Adds 129 Weapon and Spell Damage
(5 items) Dealing direct melee damage grants you Range Supremacy for 5 seconds, adding 437 Weapon and Spell Damage to your damage over time and ranged attacks. Dealing direct ranged damage grants you Melee Supremacy for 5 seconds, adding 437 Weapon and Spell Damage to your melee attacks.

Crafted in Blackwood by a Player with 5 researched traits.
With the right combination of skills, this can be rather amazing and potentially top-tier. Note that the attacks don't have to be "at range". Using a point-blank ranged attack will also work.
Some classes may struggle to find actual melee attacks to proc the Range Supremacy. Options include using Dual-wield daggers instead of destruction staff on frontbar, or Nightblades using Concealed Weapon as a spamable.

Hunding's Rage - Availability: Crafted- Difficulty to acquire: Trivial
(2 items) Adds 833 Weapon Critical
(3 items) Adds 1096 Max Stamina
(4 items) Adds 833 Weapon Critical
(5 items) Adds 299 Weapon Damage

Crafted in multiple locations once your character knows 6 equipment traits --- or have someone make it for you!
Aka. Law of Hunding's Rage; being essentially the Stamina version of the Law of Julianos magicka set. Considered by many to be a staple of stamina sets. It provides solid, permanent stat bonuses with no particular requirements on playstyle. It also serves as a good benchmark; if your stamina set performs worse than Hunding's on average, it's probably bad.
Ask a nice guild member to make you a set! It's a great starting point.

Briarheart - Availability: Wrothgarr or Guild Stores - Difficulty to acquire: Easy
(2 items) Adds 833 Weapon Critical
(3 items) Adds 1096 Max Stamina
(4 items) Adds 833 Weapon Critical
(5 items) When you deal Critical Damage, you increase your Weapon Damage by 450 for 10 seconds. While this effect is active, your Critical Strikes heal you for 349 Health. This effect can occur once every 15 seconds.

DLC required! Unless purchased
While this set has a tendency to be hyper expensive in Guild stores, it can be farmed rather easily by performing daily (world boss kill) quests in Wrothgarr. While you're at it, you might find some Pariah set pieces, which should net you a good price.
Note that the absolute maximum uptime is 66%, so the impressive 450 Weapon Damage is actually more like 300 on average. But hey! It's easy to get, and crafting Hunding's Rage rings is a pain.

Mechanical Acuity - Availability: Crafted- Difficulty to acquire: Trivial
(2 items) Adds 1096 Maximum Stamina
(3 items) Adds 1096 Maximum Magicka
(4 items) Adds 129 Weapon Damage and Spell Damage
(5 items) When you deal direct damage, you gain unerring mechanical vision for 5 seconds, granting you 100% Critical Strike chance. This effect can occur once every 21 seconds.

Crafted in Clockwork City by a Player with 6 researched traits.
This set has seen a lot of changes over the years. Changing between absolutely busted, to nerfed, to okay, to pretty good. It's currently pretty good. Getting 100% critical strike chance on a roughly 20% uptime comes out to... roughly 20% critical strike chance over all. Note that it works equally well for stamina or magicka setups.
Can be frontbar'd, which actually allows you a lot of control over WHEN the acuity procs. This means that you can time it for landing your most devastating strikes, such as ultimate abilities.

Agility - Availability: Imperial City, Daily Random Dungeon Rewards or Guild Stores - Difficulty to acquire: Varies
(2 items) Adds 1752 Maximum Stamina
(3 items) Adds 206 Weapon Damage

This is the set you use, when you can't fit another full (5)-piece set into your build. Note that they are only available as jewelry or weapons.
They're no longer the most expensive items in the game, and should be purchasable for reasonable prices, if you don't care to enter Imperial City yourself.
Note how it's a 1:1 translation of the Willpower set for magicka.

Morkuldin Arms - Availability: Crafted - Difficulty to acquire: Trivial
(2 items) Adds 1096 Max Stamina
(3 items) Adds 129 Stamina Recovery
(4 items) Adds 129 Weapon Damage
(5 items) When you deal damage with a Light or Heavy Attack, you summon an animated weapon to attack your enemies for 15 seconds. The animated weapon's basic attacks deal 4108 Physical Damage. This effect can occur once every 15 seconds.

Crafted in Morkuldin forge by a Player with 9 researched traits.
It's not top tier, as the weapon attacks a bit too unreliably. However, if you'll forgive the lapse in tryhard'nish, it's a cool set, having a glowing, golden magical weapon swerving around chopping enemies up.

Deadly - Availability: Cyrodiil vendor or Guild Stores - Difficulty to acquire: Varies
(2 items) Adds 129 Weapon Damage
(3 items) Adds 833 Weapon Critical
(4 items) Adds 129 Weapon Damage
(5 items) Increase the damage your Physical, Bleed, Poison, and Disease damage over time abilities do by 20%.

Purchased with Alliance Points from the Vlastarus gear vendor or with gold from Guild Stores.
The "secret" here is that Templar's Biting Jabs spamable also counts as a damage over time ability. Would not generally recommend for other classes.

Blooddrinker - Availability: Bloodroot Forge - Difficulty to acquire: Hard
(2 items) Adds 833 Weapon Critical
(3 items) Adds 129 Weapon Damage
(4 items) Adds 833 Weapon Critical
(5) Increases the damage you deal with bleed damage over time effects by 20%.

I actually just put this here to point out that it's a worse version of the Deadly set.

Leviathan - Availability: Crypt of Hearts - Difficulty to acquire: Medium
(2 items) Adds 1096 Maximum Stamina
(3 items) Adds 657 Weapon Critical
(4 items) Adds 657 Weapon Critical
(5 items) Adds 1528 Weapon Critical

Decent critical strike chance, and can be farmed on normal difficulty.

Strength of the Automaton - Availability: Darkshade Caverns - Difficulty to acquire: Medium
(2 items) Adds 833 Weapon Critical
(3 items) Adds 1096 Max Stamina
(4 items) Adds 129 Weapon Damage
(5 items) Adds 400 Weapon Damage to your Physical and Bleed Damage abilities.

If farmed on in the Dark Shade I version, it's not too difficult. With the right ability morphs, a stamina build can rely almost entirely on physical and bleed, making this a viable set.

Tzogvin's Warband - Availability: Frostvault - Difficulty to acquire: Hard
(2 items) Adds 833 Weapon Critical
(3 items) Adds 833 Weapon Critical
(4 items) Adds 1487 Physical Penetration
(5 items) When you deal critical damage, you gain a stack of Precision, increasing your Weapon Critical by 134 for 5 seconds, up to 10 stacks max. At max stacks, you also gain Minor Force, increasing your Critical Damage done by 10%.

DLC required!
Much like the Medusa set, this can provide Minor Force; thus potentially freeing up a slot on your ability bar and easing rotation. Frostvault is, however, not the easiest dungeon - far from it! And you may be hard pressed to farm it. Rest assured, however, that if you do get the set it will last you into late game.

Innate Axiom - Availability: Crafted- Difficulty to acquire: Trivial
(2 items) Adds 129 Weapon and Spell Damage
(3 items) Adds 1096 Maximum Stamina and Max Magicka
(4 items) Adds 833 Critical Chance
(5 items) Adds 400 Spell and Weapon Damage to your Class abilities.

Crafted in Clockwork City by a Player with 2 researched traits.
My heart says yes but my mind says no. It will do NOTHING to help important bow, dual-wield, or two-hand abiltiies abilities like Poison Injection, Rending Slashes, or Executioneer.

New Moon Acolyte - Availability: Crafted - Difficulty to acquire: Trivial
(2 items) 833 Critical Chance
(3 items) 129 Weapon and Spell Damage
(4 items) 1487 Physical and Spell Penetration
(5 items) Adds 401 Weapon and Spell Damage. Increase the cost of your active abilities by 5%.

Crafted in Southern Elsweyr by a Player with 9 researched traits.
If you can sustain through the extra costs, it's a massive bonus. Note that it works for either Magicka and Stamina.

Diamond's Victory - Availability: Crafted - Difficulty to acquire: Trivial
(2 items) Adds 129 Weapon and Spell Damage
(3 items) Adds 657 Critical Chance
(4 items) Adds 129 Weapon and Spell Damage
(5 items) Dealing direct melee damage grants you Range Supremacy for 5 seconds, adding 437 Weapon and Spell Damage to your damage over time and ranged attacks. Dealing direct ranged damage grants you Melee Supremacy for 5 seconds, adding 437 Weapon and Spell Damage to your melee attacks.

Crafted in Blackwood by a Player with 5 researched traits.
With the right combination of skills, this can be rather amazing and potentially top-tier. Note that the attacks don't have to be "at range". Using a point-blank ranged attack will also work.
Since stamina classes will typically use some combination of melee (DW/2h) and bow, both effects should be easily proc'd.

Kinras's Wrath - Availability: Black-Drake Villa - Difficulty to acquire: Medium-Hard
2 items: Adds 129 Weapon Damage
3 items: Adds 657 Weapon Critical
4 items: Adds 129 Weapon Damage
5 items: Dealing damage with a Light or Heavy Attack grants you a stack of Burning Heart for 5 seconds, up to 5 stacks. While you have 5 stacks, you generate an aura of wrath, granting you Major Berserk, increasing your damage done by 10%. While you have an aura of wrath, allies within 12 meters of you gain Minor Berserk, increasing their damage done by 5%.

DLC required!
Farm this on Normal difficulty, and you will be set for life. Easily one of the best DPS sets available within the game, per time of writing.

As mentioned, monster sets are dropped from final bosses in veteran dungeons and from Undaunted coffers. But some of the dungeons in the game aren't too hard, even on veteran - and sometimes even equipping a single piece of a monster set (that you got from Undaunted dailies) can really spice up your build.
Note here that "easy" refers to easy by veteran dungeon standards - typically still harder than any normal difficulty dungeons.
Note: Since monster set comes in all armor weight types, I'll note whether its appropiate for magicka and/or stamina.

Balorgh - Appropiate for: Magicka&Stamina - Availability: March of Sacrifices (veteran) - Difficulty: Very Hard
(1 item) Adds 129 Weapon Damage
(1 item) Adds 129 Spell Damage
(2 items) When you use an Ultimate ability, you gain Weapon Damage and Spell Damage equal to the amount of Ultimate spent, and Physical and Spell Penetration equal to 23 times the amount spent for 12 seconds.

DLC required for head piece!
March of Sacrifices is very hard, so do not expect to get a helmet piece easily. I only note this here because wearing a single Shoulder piece yields a nice damage boost.

Grothdarr - Appropiate for: Magicka - Availability: Vaults of Madness (veteran) - Difficulty: Medium
(1 item) Adds 1096 Max Magicka
(2 items) When you deal damage within 8 meters of the enemy, you have a 10% chance to create lava pools that swirl around you, dealing 1854 Flame Damage to all enemies within 8 meters of you every 1 second for 5 seconds. This effect can occur once every 10 seconds.

Vaults is one of the easier classic dungeons. This set has a relatively short range, so don't expect much use for long-range encounters. It synergizes well with the templar setup, relying on Puncturing Sweeps any way.

Iceheart - Appropiate for: Magicka - Availability: Direfrost Keep (veteran) - Difficulty: Easy
(1 items) Adds 657 Spell Critical
(2 items) When you deal Critical Damage, you have a 20% chance to gain a damage shield that absorbs 5000 damage for 6 seconds. While the damage shield holds, you deal 272 Frost Damage to all enemies within 5 meters of you every 1 second. This effect can occur once every 6 seconds and the damage scales off the higher of your Weapon or Spell Damage.

Direfrost Keep is among the easiest dungeons. While the (2)-piece bonus is more defensive, I note the set here for the (1)-piece bonus of Spell Critical, useful on any build. Combining it with another (1)-piece monster set of Spell Critical is actually very competitive - more so than some (2)-piece bonuses.

Kra'gh - Appropiate for: Stamina - Availability: Fungal Grotto I (veteran) - Difficulty: Impossible
(1 item) Adds 1487 Physical Penetration
(2 items) When you deal damage, you have a 10% chance to spawn dreugh limbs that create shockwaves in front of you dealing 1345 Physical Damage every 0.6 seconds for 2.4 seconds. This effect can occur once every 6 seconds.

Fungal Grotto I is the hardest trial in the game, and if anyone says they've beaten it they are nothing but filthy, lying khajiit or khajiit sympathizers.
Jokes aside, this is a readily obtainable Monster set with a respectable damage bonus. The only issue is the extremely short range of the Dreugh limbs, so it can be hard to land.

Molag Kena - Appropiate for: Magicka&Stamina - Availability: White-Gold Tower (veteran) - Difficulty: Hard
(1 item) Adds 129 Weapon Damage and Spell Damage
(2 items) When you deal damage with 2 consecutive Light Attacks you trigger Overkill for 6 seconds, which increases your Weapon and Spell Damage by 560 but also increases the cost of your abilities by 8%.

DLC required for head piece!
The 2 piece bonus is rather cumbersome to proc, and the dungeon is not easy. Once again, however, I mention this set because a single shoulder piece is a worthy addition to most builds for the Weapon/Spell damage.

Slimecraw - Appropiate for: Magicka&Stamina - Availability: Wayrest Sewers I (veteran) - Difficulty: Easy
(1 items) Adds 833 Critical Chance
(2 items) Gain Minor Berserk at all times, increasing your damage done by 5%.

Wayrest Sewers is one of the simpler dungeons in the game. Note that the Critical Chance is applies to both magicka and stamina skills, so it's worth slotting just for one piece. The (2)-piece Minor Berserk bonus is also solid. Plus you get to wear a crocodile on your head.

Valkyn Skoria - Appropiate for: Magicka - Availability: City of Ash II (veteran) - Difficulty: Hard
(1 item) Adds 1487 Spell Penetration
(2 items) When you deal damage with a damage over time effect, you have an 8% chance to summon a meteor that deals 5348 Flame Damage to target and 1650 Flame Damage all other enemies within 5 meters. This effect can occur once every 5 seconds and scales off the higher of your Weapon or Spell Damage.

While it is no longer the best, it's still a solid monster set. That being said, City of Ash II is one of the harder classic dungeons, so think twice before trying to farm it.