Lothario already provided good answers for most of your questions, but I figured I would add a few more tidbits.
So far my plans are to make a Breton pure mage, who will have Destructions spells for free due to gear, and capped Magic Resistance, most likely focused on Shock as a main dmg type.
Focusing on one damage type in Destruction can save you a few perk points, but I wouldn't recommend it. You'll want each elemental type at full power for when you're facing an enemy that's weak against or resistant to a school, and it's generally more fun to have them all at your disposal. You also shouldn't be short on perk points playing a pure Mage.
His main spell lines will be Dest, Conj, and Illusion, unless alteration is really neccesary?? I was hoping some of the more experienced pure mages could impart some knowledge on me.
As Lothario mentioned, Conjuration and Illusion fulfill the same basic function in combat-- crowd control. I recommend Conjuration over Illusion because Illusion requires a heavy perk investment and 4 x Fortify Illusion enchants to remain viable, whereas Conjuration only need 5 perk points, and is less mana intensive. On the other hand, Illusion is more compatible with Magic Absorption if you want to go that route and can't mod out the bugs on PC.
I was wondering, if you have 80-85% magic resistance, is it still neccesary to have very high Fire/frost/shock resistance as well?
Necessary? No. But if you're playing on Expert or Master, 80% Magic Absorption or significant Elemental Resistance will definitely make a noticeable difference in your magic mitigation.
Any recomendations for gear? I want to wear robes, and I figure 3-4 enchantments will be taken up by Fortify Destruction enchanments. Besides that I have no ideas really.
You'll want at least 8 points in Enchanting (5/5 Enchanter, Insightful Enchanter, Corpus Enchanter, Extra Effect; or, if you plan to cap Elemental Resistance, skip Corpus Enchanter in favor of Fire, Frost, and Storm Enchanter) so you can enchant your cloth or armor to two sets of 4 x Fortify
(25) for free casting in two spell schools. You'll be best served by zeroing out mana cost for Destruction and Conjuration or Illusion (whichever you picked for crowd control).
What is the best way to mitigate physical dmg? Are the flesh spells and alteration perks that increase them very neccesary/ really that good?
You can either perk Smithing + Light/ Heavy Armor or heavily perk Alteration and wear cloth. The former provides the best mitigation, as you can easily hit the armor cap with as little as 3-4 perks invested, but the latter is a more Magey option that offers other benefits as well, since Alteration offers more than just defense.
To help you compare, you I'd recommend one of these two options: (1) 2 points in Smithing (Steel, Elven) and 3 in Light Armor (1/5 Agile Defender, Custom Fit, Matching Set) allows you to craft an armor capped (80% mitigation) set of Elven armor which weighs only 7 lbs total; or (2) fully perk Alteration (14-15 points), which will cause your Ebonyskin spell to grant 300 Armor (48% mitigation) for 4 minutes, along with lots of other benefits. Toss in the Lord Stone to bring your Armor up to 350 (54%).
Those other benefits include: (1) Dragonhide, a master level Alteration spell, which caps your physical mitigation at 80% for 1 minute; (2) Paralysis; (3) Detect Life; etc. I favor wearing cloth perking Alteration because it's more a Magey option that keeps the game somewhat challenging and offers lots of other useful spells, but if you want maximum mitigation at all times, Smithing your own Elven armor is the way to go.
Also one thing that has been bugging me is how difficult is it going to be to level Destruction, and reach a level where my enchanting can lower the cost of Dest spells enough, without taking the apprentice/adept/ etc, Dest. perks?
Level your Enchanting ASAP, and then Skill up Destruction on Shadowmere or the Companions NPC that spars with you.
I'd recommend http://skyrimcalculator.com/#26172 if you want to use Alteration for defense, and http://skyrimcalculator.com/#26173 if you want to wear armor.