Pure mage:
Destruction, Alteration, Conjuration, Restoration, Illusion in that order.
Destruction will be you main attack. Take nearly all the perks in destruction except for Rune Master, Intense Flame and Deep Freeze.
Alteration: Your main defense. All the perks are good here. DragonHide will be your armor. Or you can play Heavy BattleMage and go Heavy Armor and drop alteration. Your call.
Conjuration: Your decoy. Summon Dremora Lord for them to take the aggro in melee when you spam your destruction spells. No need for Bound weapons. Twin Souls will help. 2 dremora Lord are very hard to beat.
Restoration: Healing and Magicka regen. Cast Ward, and get Ward Absorb, so every spell cast at you regen your Magicka pool.
Illusion: Just for Crowd control with spells like Calm, Frenzy, Pacify. Quiet casting perk is NOT necessary, you won't be discreet anyway.
If you go the Alteration way, you will wear Clothes. If not, then get heavy Armor. Get your gear enchanted with Magicka reduction cost mostly for Destruction and Alteration (if you use it) then for Conjuration. Otherwise your magicka regen will do the rest.
Get 400 Magicka and 600 health, with 100 stamina (level 81). Go Magicka 2 and Health 1 till you get 300 magicka. Then switch 1/2 till you get 400 magicka. Put the rest in Health only.