just to piggy back off the great info @ Armitas provided, you can use a melee weapon for a magic build but it will not restore your magic. You do get greater spell damage and spell power from melee weapons (dual wield and 2h sword) then you do from staves but the trade off is that you will be missing range and magic restore. Stamina on a magic build is used more for defensive purpose than anything else, it allows you to roll, block, run, and break free; conversely Magic on a stamina build is used for the same reason except that you will be casting magic for the defensive class skills, i.e. obsidian shield, spiked armor, reflective scales, etc. DK is unique in that we can effectively play a hybrid (without having to split attributes to do so) because most of our skills are defense based. So if you play stamina for example, you can load all your attribute points into stamina and health (or all stamina) and use any of the many defensive magic skills to bolster your defense. Since a good amount of these magic skills have long duration on them you can cast them with the small magic pool you will have from being stamina and still get the full effect. Only offensive class skills scale off magic so if you play stamina I'd avoid those.

If you are a magic build and decide to use melee weapon (I recommend this by the way) you need at least one staff (either resto or destro). Your magic spells will hit harder from your melee weapon and you can use the staff to pick some extra magic when needed. Plus since the staff gives you range options it will be the best way to engage long range targets until they get into the DK's melee range. Realize that as a DK, most of your class skills, especially the offensive ones, are melee range so you will need to go into some sticky situations in light armor, but that's where those defensive magic skills will really shine, as with a magic build you can spam them to your need with little consequence. As a magic build you also have access to constant heals from a number of sources, Igneous shield (morph of obsidian shield) gives 30% increased healing, Inhale steals health from surrounding enemies then deals an AoE, burning embers (morph of searing strike) gives a direct heal based on damage done, Flame lash (morph of lava whip) gives heal over time of set amount of damage, and in pve Green dragon blood/Coagulating blood (morph of dragon blood) restores up to 33% of your missing health, gives a 20% health recovery bonus, and depending on which choose you get 20% stamina recovery or an additional 8% increase to healing received (coagulating blood stacks with draconic power passive "burning heart" which give up to an additional 12% healing increase, and the 30% from igneous shield....the result of which is amazing)

In short regardless on which way you decide to go, magic or stamina, your DK will be tanky and have great utility for survival. Hope this helps and if you need more specifics, give more detail about your character and how you intend to build and I am sure we DK's can share our experience with you. Good luck!

You can heal effectively with stamina heals like rally and vigor. If you are looking to PvE as a magicka DK dps go with the inferno staff, elemental drain will handle any amount of magicka concerns.

In regards to magicka recovery try to set your gear up so it benefits you with the magicka recovery, so equip any jewelry that has magick recovery or reduced cost of spells, if you can craft set gear that gives bonuses to magicka recovery do it

My set up is magicka DK dps all heavy armour (so i have bonuses in health), i am wearing 5 set Seducer & 4 piece Magnus Gift with duel wield swords. Having the duel weild doesn't mean i use any of the skills in that skill line, it's only for my light & heavy attacks. Because I'm a magicka build i don't want stamina skills they will be to weak