I don't consider it a "Pure" mage build with armor, and weapon skills. That's a Spellsword, or Battlemage. I've made Pure Mage work, but only by focusing on 3 skills for the most part. Conjuration, and Destruction on offense, and Illusion on indirect defense. The idea is with Fear, Calm, and Frensy, you can keep everyone too busy to target you while they're fighting your summons, and taking AoE damage. That is, untill you get to Invisibility, then you're pretty much a bystander throwing damage in.
Start with Altmer, for the highest illusion bonus, only stat bonus, and fastest running speed. You will not be sneaking, but running around in robes, with nothing but magic in your hands, so nothing can catch you. I suggest you at least Destroy the Dark Brotherhood for the Shrouded Shoes, so you don't have to cast Muffle, then spam Fury like there's no tommorow, and keep Calm handy in case something comes your way. Burn any survivors. Concentrate on Destruction until you can Augment Flames (30-60) and cast Ice Storm (60). Now, the hard part.
Kill Vokun. Look it up, if you don't already know this one, the quest is called A Scroll for Anska, at High Gate Ruins. His mask is nice, a lot of armor, plus 20% off Conjuration, Illusion, and Alteration spells. The big payoff is the quest reward, a unique spell called Flaming Familiar. This little buring wolf runs in, gets a couple bites in, then explodes in a fireball after about 6 seconds, if he's not destroyed first. One thing that can set him off in one shot is Ice Storm. Now, there is nothing in the game that is resistant to fire, and frost, and both are AoE, so anything in the blast radius is either dead, or slowed, and on fire. You can cast it again.
Here's the thing, Flaming Familiar will run around cover, and Ice Storm goes right through it, so you don't even have to expose yourself. A solid wall, or even the bitmap is better than capped out daedric for any, and all damage, you can hit them, they can't hit you. If you really must directly interact with the enemy, you can teabag them when they're dead...
What I usually do is lead with Frenzy, and Invisibility. This gets everbody clumped together while you recharge, and get in position for the finisher combo. Level dependent, this works on everything, except Dragons, which require completely different tactics. For them, I use a Ward(absorb), and Lightning. The latter is a hitscan, so you don't need to lead, and dragons aren't resistant to it. The former can be perked to soak up all damage from the breath attacks, to power the bolts. Don't keep the shield up the whole time, it will run you dry, but you can time it, since they always pause after Yol... (or whatever) then let loose the shout.
So, at that point, you have to switch to Nahkriin, for the antidragon combo. Both masks count as Heavy Armor, but you can truly avoid getting hit so you don't earn any experience in it. That way, you can stay a pure mage, and beat anything in the game... 4 skills, no crafting, armor, stamina, nor health investment. Of course, you have to think, and manage your energy, but isn't that what being a Pure Mage is all about?