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Proc free DPS build for when a tank isn't holding bosses in place and for times where one is not getting buffed by a healer.
Gear: 5 Netch's Touch (All apparel Divines with Max Mag Enchants), 2 Slimecraw (All Divines. 1 med/1 heavy. Max Mag Enchants), Maelstrom's Lightning Staff (infused/shock enchant), and Infallible Aether jewelry (arcane with spell damage enchant)/lightning staff (infused/flame enchant).
Ability-Bar 1: Critical Surge, Boundless Storm, Mages' Wrath, Hardened Ward (Twilight Tormentor if one can somewhat trust both the heals and tank to keep you alive), Lightning Flood, and Power Overload.
Ability-Bar 2: Dark Deal, Streak, Shock Reach, Dampen Magic (Twilight Tormentor if one can somewhat trust both the healer and tank to keep you alive), Unstable Wall of Storms, and Thunderous Rage.

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DPS build for more organized groups.
Gear: 5 Burning Spellweave (All apparel Divines with Max Mag Enchants), 2 Grothdarr (All Divines. 1 med/1 heavy. Max Mag Enchants), Maelstrom's Inferno Staff (infused/shock enchant), and Infallible Aether jewelry (arcane with spell damage enchant)/lightning staff (infused/flame enchant).
Ability-Bar 1: Critical Surge, Boundless Storm, Mages' Wrath, Hardened Ward (Twilight Tormentor if one can somewhat trust both the heals and tank to keep you alive), Lightning Flood, and Power Overload.
Ability-Bar 2: Dark Deal, Streak, Flame Reach, Dampen Magic (Twilight Tormentor if one can somewhat trust both the healer and tank to keep you alive), Unstable Wall of Fire, and Fiery Rage.

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Utility focused DPS build that is capable of tanking normal dungeons and vet non dlc dungeons, but it does not provide enough tank based buffs/debuffs to warrant it's use in trials/vet dlc dungeons and due to the limits of damage shields it would be too much of a liability due to the sheer number of potential one-shot mechanics that a pure tank would have an easier time dealing with.
Gear: 5 Icy Conjuror (All apparel Divines with Max Mag Enchants), 2 Iceheart (All Divines. 1 med/1 heavy. Max Mag Enchants), Maelstrom's Ice Staff (infused/ice enchant), and Infallible Aether jewelry (arcane with spell damage enchant)/lightning staff (infused/flame enchant).
Ability-Bar 1: Critical Surge, Boundless Storm, Mages' Wrath (Elemental Drain in vet content if healer isn't using it), Hardened Ward, Lightning Flood, and Power Overload (Replenishing Barrier when healer isn't keeping others alive).
Ability-Bar 2: Dark Deal, Streak (Inner Rage when dealing with multiple bosses), Frost Reach (Restraining Prison when I want to lock enemies down), Dampen Magic, Unstable Wall of Frost, and Icy Rage (Aggressive Horn when DPS is decent).

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My healer build that I for the most part only use in normal dungeons/trials or in Vet premades, since playing with randoms tend to result in me being in a group that lacks DPS, has a fake tank, or both.
Gear: 5 Spell Power Cure (All apparel Divines with Max Mag Enchants), 2 spell critical monster set pieces when I don't feel like using spell crit pots, Grothdarr when I want to do more damage, Bogdan when I want more HoTs, Symphony of Blades to provide more emergency resources, or Earthgore when I feel like it would make a significant difference (All Divines. 1 med/1 heavy. Max Mag Enchants), Maelstrom's Lightning Staff (infused/shock enchant), and Infallible Aether jewelry (arcane with spell damage enchant)/restoration staff (infused with weapon damage enchant).
Ability-Bar 1: Critical Surge (Power Surge for more heals), Boundless Storm, Combat Prayer, Ward Ally (Twilight Matriarch for another burst heal and damage), Energy Orb, and Replenishing Barrier.
Ability-Bar 2: Dark Deal, Overflowing Altar, Elemental Drain, Hardened Ward (Twilight Matriarch for another burst heal and damage), Unstable Wall of Storms, and Aggressive Horn.

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Tanky utility focused PvP healer that can take down very inexperienced players, but is primarily focused on working alongside others in an organized group, PUGs, or zergs.
Gear: 5 Torug's Pact (3 heavy body pieces, light waist, and medium hands. All Impenetrable. Max Mag Enchants), 2 heavy Mighty Chudan (All Impenetrable. Max Mag Enchants), and Knight Slayer jewelry (arcane with spell damage enchant)/lightning staff (infused with oblivion enchant)/restoration staff (infused with oblivion enchant. Same enchant as lightning in order to maintain consistent pressure regardless of which staff you're heavy attacking with). [When more focused on damage will change Chudan pieces to medium and light. Also all my Torug body pieces to light except the chest that stays heavy].
Ability-Bar 1: Structured Entropy, Consuming Trap, Haunting Curse, Ward Ally, Rapid Regeneration, and Life Giver (or Soul Assault).
Ability-Bar 2: Dark Deal, Elusive Mist, Rune Cage, Hardened Ward, Efficient Purge, and Shooting Star.

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Damage shield tank designed to help my guildmates clear vet dungeons when a typical tank isn't available.
Gear: 5 Brands of the Imperium (All Divines with Max Mag Enchants), 2 Mother Ciannait (All Divines. 1 med/1 light. Max Mag Enchants). Combat Physician jewelry (arcane with spell damage enchant)/Ice Staff (infused/crusher). Blackrose Restoration Staff (doesn't have to be the perfect version. infused/hardening enchant).
Ability-Bar 1: Critical Surge, Bound Aegis, Inner Rage, Boundless Storm, Ward Ally, and Replenishing Barrier.
Ability-Bar 2: Deep Thoughts, Bound Aegis, Restraining Prison (Elemental Drain in vet content if healer isn't using it), Unstable Wall of Frost, Hardened Ward, and Temporal Guard.

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Gear: 5 Law of Julianos (heavy chest, gloves/belt light, and the rest can be light or 1 medium piece if you're not wearing medium anywhere else on your body. All in training if grinding for XP or divines), Armor of the Seducer or Magnus' Gift head, shoulder, and staves (light with 1 medium piece if you are not already wearing 1 medium Julianos piece. All in training or divines. The staves should be training or infused), and 3 purple Willpower Jewelry with Arcane trait (can be bought from trading guilds for relatively cheap. Check tamrieltradecentre.com for the best deals if you're not using a price checking addon).

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High elf, since you will not have issues with sustain, but other mag based races are also fine so this is more of a personal choice.

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PvP: The Atronach.
PvE: I will almost always use the Atronach in this content as well (especially if I'm healing in PvE or playing it safe while solo). However, in a strong group other Mundus Stones can be effective (Thief is what I would use in a serious group as a healer. As DPS I would use Shadow or Lover depending on group), since a heavy attack rotation will ensure that you're always restoring magicka at a decent rate. When using electric-ward in vet content I will always use the Lady to reach 25k+ physical/spell resistances.

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Mag Sorc: More focused on damage, since changing CP isn't free. Mage: Elfborn (56), Spell Erosion (22), Elemental Expert (64), Staff Expert (44), Master-at-Arms (9), and Thaumaturge (75). Warrior: Ironclad (34), Resistant (8), Light Armor Focus (12), Hardy (32), Elemental Defender (32), Thick Skinned (31), Expert Defender (33), Bastion (56), and Quick Recovery (32). Thief: Warlord (31), Sprinter (6), Bashing Focus (6), Arcanist (75), Tenacity (75), Shade (25), Tumbling (26), and Shadow Ward (26).

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Mag Sorc: (In your gameplay settings turn on quick cast ground abilities) Buff up with Boundless and Surge, weapon swap immediately after casting the previous skill, drop Rage if it's active (only drop it on significant bosses or in situations with lots of enemies where you know you'll have the ult filled up by the next boss), Reach, Unstable, quickly weapon swap, Liquid Flood, two heavy attacks, activate either Surge or Boundless, cancel the animation of the buff used with a weapon swap, and repeat. If you have an excessive amount of ult and you're dealing with trash mobs activate overload before performing the rotation, but don't heavy attack for too long. If you have enough ult for Rage while you're fighting a serious boss and you're in the middle of the rotation just focus on activating the ultimate, afterwards either continue the rotation or start from scratch. During the execute phase (around 20% health) replace the second heavy attack with about 4 Mages' Wrath, but if boss is melting quickly just keep spamming Wrath (hold heavy attack while spamming Wrath). When using Twilight Tormentor only use the active ability before a fight and at times where you aren't actively engaging the boss.

When frost staff tanking a single boss buff up with Boundless and Surge, weapon swap immediately after casting the previous skill, heavy attack with the ice staff, drop Rage if it's active, Reach/Restraining (at times can be replaced with an additional lightning staff heavy for sustain), Unstable, quickly weapon swap, Lightning Flood, one heavy attack (two if Reach isn't used), activate either Surge or Boundless, cancel the animation of the buff used with a weapon swap, one heavy attack, and repeat. If frost staff tanking multiple bosses buff up with Boundless and Surge, weapon swap immediately after casting the previous skill, heavy attack with the ice staff each enemy, drop Rage if it's active, Unstable, quickly weapon swap, Lightning Flood, heavy attack priority boss in order to proc IA (pink smoke), activate either Surge or Boundless, cancel the animation of the buff used with a weapon swap, heavy attack all the bosses, and repeat. Can also slot in Inner Rage and forego heavy attacking with the ice staff. If using inner rage after getting aggro perform the DPS oriented rotation and retake aggro after 1 rotation. Most challenging bosses to keep aggroed will be the Pact in the Blessed Crucible and the knights in the White-Gold Tower, since you need to keep 3 enemies taunted, but they can also be locked down with Restraining. During the execute phase on a single target (around 20% health) replace the second heavy attack with a partial heavy attack in order to proc IA and around 4 Mages' Wrath, but if boss is melting quickly just keep spamming Wrath (hold block while spamming Wrath).

When healing in PvE just keep all support skills and Unstable up. Heavy attack primarily with a restoration staff whenever you can. Be reactive with your heals (when someone is scratched use ward ally and top them off with some Prayers). When taking a lot of continuous damage make sure to have all buffs/debuffs up while keeping Energy Orb active in the group. At the boss use the horn ult, but only when the group has decent survivability and damage. If too many players lack survivability then use the barrier ult to make life easier (longer fight, but less risk of death). Can use barrier when dealing with trash mobs (gives back ult).

In PvP you'll rarely be in a scenario where you can perform a PvE esque rotation with AOE unless you're performing a single target burst. For the most part just stun peeps whenever possible, apply dots, and heavy attack them a few times. Rinse and repeat till they die and use ults as needed, but make sure to keep your health and shields up whenever you take significant damage (might have to keep one's distance if a dk is using a skill like draw essence). When in a high pressure situation stay on the lightning staff bar and keep hardened ward up while stunning and heavy attacking hostiles make sure to keep primary buffs up, heal up, purge, and shield stack as needed. When dealing with a large amount of enemy players alongside your faction keep your distance from friendlies (avoid bombs). If you get debuffs on you be careful not to overuse efficient purge, which is still quite costly. If not grouped up do not bother using purge on a debuffed friendly, since it will not affect them at all.

In PvE and PvP make sure to utilize tab target to keep track of priority enemies. Use streak in PvE for mag based movement that also allows you to stun a group of enemies. Use elusive mist for mag based movement, snare removal, and damage mitigation in PvP (can also be used in stealth, but will pop you out of a hidden state for a brief moment).

In PvP when solo taking a resource ride your mount towards the tower, aggro the two guards at the front of the entrance, then head on inside the tower, buff up, purge, head up the stairs, kill everyone that follows especially the mage guard, kill everyone on the flag, and flip.

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Gold Food for PvE:
(DPS) Corrupting Bloody Mara (increases Max Magicka by 4620, Max Health by 5051, and Health Recovery by 505 for 2 hours). If a vampire use font of loss furnishing to decrease vampirism to stage 1 to benefit from health recovery.

Gold Food for PvP and PvE:
(PvP healer/PvE serious tank) Clockwork Citrus Filet (increases Max Health by 3326, Health Recovery by 406 [useful if stage 1 vampire], Max Magicka by 3080, and Magicka Recovery by 338 for 2 hours).

Trash Potions when feeling cheap:
Regular CP150 Essence of Magicka pots that I obtain frequently from playing the game or Crown Tri-Restoration Potion obtained from dailies.

Crafted Potions:
Essence of Spell Critical (Bugloss, Lady's Smock, and Water Hyacinth). Without magelight this is my primary means of obtaining Major Prophecy, which increases my Spell Critical Rating. This also heals and restores magicka. Essence of Immovability (Columbine, Corn Flower, and Wormwood). I use this in PvP, since this gives me stealth detection, knockback immunity, and restores magicka (better to use it when competent allies are nearby, since it might reveal that you are surrounded by multiple players in stealth and you will not have an emergency pot available after use). Essence of Invisibility with only 2 ingredients (Blue Entoloma, Namira's Rot, Nirnroot, or Spider Egg). I use this in PvE content that requires stealth and if I need more speed I'll use Rapid Maneuver before using the potion. Essence of Invisibility with 3 ingredients (Blessed Thistle, Blue Entoloma, and Namira's Rot). Very useful in PvP alongside the vampire Dark Stalker passive, since you'll be invisible, ignore movement speed penalty while in Crouch, and you'll have a 30% movement speed boost from Major Expedition (I always have this slotted when riding from point A to B in PvP land, since gankers are always lurking).