Stop sneaking and hit them with spells. Also you don't have impact yet. You need impact! Impact will give you a guaranteed brief stun on enemies when destruction spells are dual cast. This is what keeps you alive!
Ward is how you deal with enemy mages, not magic resist. It is massively spendy for now, but will be affordable much sooner than the three perks necessary to give you half off for incoming damage. If you find mages that awful a burden to bear, hunt down a ring of magic resist or some specific damage resist gear.
Mages are almost more gear reliant than physical type characters. You need stuff to reduce the cost of your primary damage line or you will die die die. Not regen stuff, you want cost reduction stuff. Regen is irrelevant and pointless and simply cannot keep up with the huge advantages of cost reduction. My character in the mid 40s can, with his gear on, spam dual expert destruction spells basically without any limit, and can fire off the rituals effortlessly. Without his gear on, he can maybe do ten or twenty and can't really sustain the rituals for any serious amount of time.
Regeneration is a mostly pointless talent, you shouldn't take it. The Adept level healing spells will blast you for 150hp easy, which you should really never need. I mean even if you dump half your level up rewards into health between zero and 40, you'll only hit 300hp. You do not need a spell that heals for more than your health, and the spell in question is fairly cheap.
Alchemy sucks compared to enchanting. Potions are common and plentiful, gobble them rather than making your own in the early game. You can use it to buff your enchanting skill, but blowing talents on it during the early game is a bad idea.
Adept level destruction spells will be your bread and butter spells. On adept difficulty you can probably rely on them for serious damage against mooks well into the 30s (on master they're mostly convenient aoe stuns by that point unless spammed heavily). Race up the destruction tree to get them if you really want to use magic.
Armor is entirely viable for mages. If you find you need more physical protection than the spells provide you should grab light armor and perk up to the weightless one. That'll cost you 3 perks and require you to hit 50 in light armor. You'll get better defense but you'll also be slower. It's also harder to get a chest piece with cost reduction than it would be for a cloth mage, but that's the tradeoff.
Alteration is weak in the early game, but when you hit expert it will be one of your best schools, if not the single best. This tree has paralyze, detect life/dead, all the armor spells, transmute, and a few other handy things. It is godly.
Illusion is strong in the early game, but gets progressively weaker from what I can tell. Even invisibility isn't all that great. Grabbing a few low level frenzy and calm spells will give you an edge against mooks for a long while, but I'd be wary of overspending on perks for stuff that won't scale very well. Of course I didn't get the dual casting perk for Illusion, so I dunno!
edit: And if you want a mix build, I'd recommend going heavy armor, sword and shield and just plowing through shit like a bashing boss.