What armor for a two handed battle mage?
Solution 1:
If you're going for a tank build (stand there, violently attacking and taking tons of damage) go heavy. This would be melee > magic.
If you're going for a kiting build (run around, fire off spells, then run in and attack) go light armour OR (IMHO a better option from what I've seen; the stat boosts are huge) enchanted robes of something. This would be for a magic > melee build.
And if you're looking for bonuses, I believe they are equal. If not, just enchant your own.
Solution 2:
About that guy who said light armor is useless...
The armor cap (537 or 567) can be achieved with either light armor or heavy armor given the right perks and smithing upgrades, rendering the argument that heavy armor provides more protection absolutely mute (in upper levels).
The heavy armor tree is bloated with wasted perks such as: fist of steel and cushioned which provide no benefit to a two handed battle mage and simply waste your perk points.
There are no useless perks in the light armor tree. You get the incredible wind walker perk, which increases stam regen by 50% (!!) when wearing all light armor. For any two hander build, this is incredible and far outwighs the Tower of strength bonus from the heavy armor tree. (the only real difference between the two maxed out trees and when both hit the armor cap is the Wind Walker Werk vs. Tower of Steel perk as both have perks that reduce weight when worn to 0 and can hit the armor cap.)
Warning: If you want to have fun with Skyrim and not worry about Min/Maxing every single little detail please turn back now for sanity's sake.
Here is my personal Two handed battlemage build: http://skyrimcalculator.com/#58704
Notice which perks I took for Alchemy, Smithing and Enchanting (for the maximum enchantments/smithing/potions stacking effect as shown here: http://elderscrolls.wikia.com/wiki/Enchanting_%28Skyrim%29).
It may seem counter productive that I went up the heavy armor side of the smithing tree after speaking on the benefits of light armor. But remember that Dragon armor allows you to craft the BEST light armor set in the game, no matter which side of the smithing tree you went up. Plus, I get to make Daedric weapons, the best weapons in the game.
Some other notes:
Block Tree: The right side of the Block tree where all the bash perks are + quick reflexes, ARE usable when wielding a two handed weapon (and quite necessary if you ask me). Interrupting a power attack in slow-mo has saved my life countless times.
Two Handed Tree: According to what I read from what little theorycrafting has been done so far, the weapon specialization bonuses (Limb splitter, Deep Wounds, Skull crusher) are actually far weaker than they initially look at first glance and provide only minimal damage increases, so that's why I skipped those.
Destruction Tree: Chose to specialize in 1 type of destro spell. Also note I skipped Apprentice - Master Destruction perks that halve the cost of magicka as I intended to enchant for -100% cost of destruction spells (4 items x -25% cost per item) in order to cast destruction spells for free.
Alteration: jumped in here mainly for the 30% absorb magicka perk and the 10%/20%/30% margicka resistance perks. I am a breton so when I added up the blessing of mara (15%) + Breton Racial resistance (25%) + Lord Stone (25%) for magick resistance, turns out I only needed 20% more from alteration to hit the magicka resistance cap (which is 85%, cant be completely immune like in oblivion).
For best results with this build, choose a Breton (or high elf).
The other perks should be self explanatory.
OR: ignore everything I said and just have fun with your character and don't worry about it!
Solution 3:
If you're going for the robes (no armor) route, there's a nice perk in the Alteration tree to support this.
Basically it multiplies the effect of Armor spells, starting with 2x for rank 1 (3 ranks in total), but only if you're not wearing ANY armor.
This has the advantage of giving you a very high armor rating, plus the insane magicka regen you get from wearing robes. Of course, if your armor spell runs out... you're down to 0 armor again, so be careful!
Solution 4:
Maybe a switching armor method, as that when casting use quick access to get into robes and heavy armor, and when enemy is close enough quickly change into heavy armor and two handed. Another method is a robe plus heavy armor component, like heavy armguard and helms, which provide some armors.
However, the best method is to disenchant the robes and put enchantment onto heavy armors, like Daedric armor with fortifying magicka regen and destruction. One thing is certain - that light armor is useless.