A Battlemage is basically a Destruction mage, so put in as many perks as you can into that skill and dual wield spells. I wouldnt use armor, but instead take Alteration. Conjuration and Restoration would be ideal as well. Just invest a few perks into One-Handed for back-up.

I play, dunmer,

Heavy armour - Juggernaut 5/5
one handed - 100% stronger - 5/5 (cant remember name)
destruction - Fire spell boosts - rune master - and the fire spell enhancer
restoration - some sweet perks in here, they restor stamina as well as health at one point!

I basically shoot a fire rune with the 5x further perk, blitz them with fireballs etc till the get to me and usually i can finish them off with my war axe in my other hand. If for some reason there not going down, I then just summon a bound sword on my off hand for some quick extra damage, then heal afterwards. It works well, Im not to keen on the bound weapons because they are a pain when they disapear in the middle of a battle. Plus later on in the game I believe there not as powerful as many other enchanted versions of the deadric base they are set upon. Hope this helped at all?