race: Khajiit - 22 additional demage because of claws
You'll need to find http://www.uesp.net/wiki/Skyrim:Gloves_of_the_Pugilist gloves in ratway - recommend to go find them right after Unbound quest - enemies are easyier to kill
for the mage part - recommend to level alteration magic to 100 as soon as possible and via winterhold mage school learn spell http://www.uesp.net/wiki/Skyrim:Dragonhide
also restoration magic isn't useless with that perk that can heal you 250 points once per day
About shouts, very helpful shout for this build should be slow time or disarm
due to skyrim's obscenely nerfed spell system there's only so many a mage has at their disposal. start buying, finding and using them. as you gain skill you'll gain access to better spells.
alt spells for armor. illusion and conjure for control and fun.
staff for powerful spell attack without using magicka.
pay for training.
as you play, you'll be able to see what style suits you best and then you begin to specialize.
and yes.. I almost forget... here take some http://images.uesp.net/c/c4/Fishystick.jpg
well, ok breton should be fine but if not khajiit it should be at least argonian - beast races have bonus to unarmed and they have very fun gameplay too
go to that winterhold school of magic (or something like that) and do their main quest - during that you will find spell http://www.uesp.net/wiki/Skyrim:Detect_Life_%28spell%29 - when you find it, go to riften or some place with lot of npcs and start dual casting it - this is my way and it is pretty much fast I guess
EDIT: very recommended is use http://www.uesp.net/wiki/Skyrim:The_Lord_Stone standing stone ability (+50 armor and 25% magic resistance)
I've played one true mage and it was tough at first, but I ended up really enjoying it. I hung around Whiterun until I built up enough strength to travel and hire a follower. Then I headed to the College. I also had a drinking contest with Sam as soon as I found him and ended up with a most useful item. A follower and a summond bad guy keeps you shielded while you pepper the enemy with spells. Conjure armor and weapons and work towards cost reduction for your most used spell categories.
Be prepared to run. Especially early. If you play a true robe wearing mage, you will be squishy. This is about as opposite of a play style as you can get from melee and archery. At least in my opinion.
Nope, Argonians have +6 do unarmed demage - http://www.uesp.net/wiki/Skyrim:Argonian
I've always played pure mage, Breton. I use mostly destruction and summon to survive early on. Never has been a problem. I can take down a dragon with no MAJOR problem. I keep plenty of health and mana potions at my disposal and have Macurio tagging along as well. We are unstoppable.
https://www.youtube.com/watch?v=HNIdFPlD_Yw
You can find telekinesis spell book in Red Water Den (but you need Dawnguard DLC).
Well, this is more like loop then tutorial, but yes, you can do this too
Depends how you want to do it really. You can go enchanting and make all spells cost 0 magicka (gets boring trust me). Me personally I always went alchemy for magicka restore potions and went Altmer and just tried to get it as high as possible. Destruction is not the greatest spell school though.