Get a follower who is a good fighter so they can draw then attention of the enemy while you blast them with spells. I prefer clothing for my mages and enchant it with fortify magicka or fortify magicka regeneration. Having a nice offensive staff as a backup in case you run out of magicka is a good idea too.
Look at destruction (pay attention to secondary effects of the spells!), conjuration (insta tanks), restoration (heals, some offense with dawnguard), illusion (invisibility, frenzy, calm), alteration (lots of useful spells, including the skin/armor spells)
A pure mage would be in robes/clothing (all enchanted):
Good enchants for general use when you can do your own:
Hood or Circlet : Fortify Magicka, Fortify Magicka Regeneration
Chest : Fortify Destruction and Regeneration, Fortify Alteration and regeneration (aka fortity school and magicka regen enchants)
Gloves : Fortify Magicka, Fortify Carry Weight (not likely putting much into stamina)
Shoes : Fortify Stamina, Fortify Stamina Regeneration (for sprinting and carry weight)
Ring: fortify Magicka, Fortify Magicka Regeneration
Neck : fortify Magicka, Fortify Magicka Regeneration
I prefer this setup to stacking fortify school enchants. Because it works out about the same, but benefits all the schools. The stamina and carry weight enchants are great since you likely will have very little put into stamina (with magicka and health being primary concerns). Sure you're not using 0 cast spells, but ya got a pool of magicka that is very nice.