I've played nearly every class that you could play in Skyrim.
My favourite build for a Battlemage is :
Heavy Armor (for the higher levels), One Handed (for Dual Flurry if you are stuck in a sticky situation), Conjuration (for bound weapons), Destruction (obviously), Enchanting and the rest is up to you.
Put as many points as you can into Magicka in the beginning and try to farm sould.
Get Azuras Star and make it black
Spoiler even tho the game says that you can't get white souls with it you can still do that
because every Mer, Men, Argonian and Khajiit has a black soul and black souls are just like Grand souls.
Level up Enchanting as fast as you can and make items that give you more Magicka, faster recharg time, less cost for Spells etc.
Get the Archmage robes and a Dragon Mask that is made for mages.
Later in the game when you have a higher level and have loads of Magicka, get a strong armour (ebony, dragon or daedric) and enchant it. Your gauntlets should higher your one handed damage so you can destroy stuff even faster
Now you have to choose between more magicka or more health.
If you want to stay alive a little bit more stick to magicka but if you want to be a tanky mage then get health enchantments.
PS: Dual Flurry bound swords can kill a Dragon (even Alduin on master!!!) in less than 5 standing power attacks.
Hope that helps you out, and here you have some bunnies
