With Battlemage I mean somebody who uses heavy armor and most often destruction magic.
But one question. Which fighting style to choose? Should I focus especially on magic and use dual wielding magic? Or should I balance warrior/mage and use a weapon in one hand and in the other hand spells? I think both are very viable, but I am not too sure myself.
My character will also be a Vampire and Dark Elf, if that makes any difference to this choise.

I'd say stick with magic.
If you want to use a weapon, Use the Bound Sword in the conjuration tree. Upgraded its as good as a Daedric Sword.

I made a Battlemage character that wore Ebony Armor(and a Apprentice Hood). Using the Adept Destructiion spells like Fireball/Chainlighting/Blizzard and the bound sword you are nearly unstoppable even on master difficulty.

I also enchant my armor to increase my Magicka. I would occasionally use a Ebony hand Axe(fire enchanted) if the bound sword wasn't cutting it.


Race doesnt matter too much. I personally like the Breton because of the magic resistance (perfect anti-mage)
Use the Mage Stone at first, and around level 15 switch to the Lord or Atronach Stone

I prefer to go with a melee focus more on my Battlemage, for the sole reason that magic typically doesn't cut it in fights. I usually end up burning all of my mana weakening my opponent, and then finish them off with my melee weapon (I myself use two handers, but one handed obviously works fine).

You have a good point, but I was thinking about creating a certain weapon with a magical enchantment and giving it a special name for the roleplay. But that would not really make that much sense if I don't really focus on melee combat that much.

i usually play spellswords, using magic (conjuration & destruction ) and melee (no conjured weapons) aproximatly the same. the coolest combination is with 1h dual wield BUT to change all the time in between spells and your two 1h weapons (two different ones) is a pain in the ass (sorry to say it like this but that discribes it very accuratly). so if you want to go for a "real" weapon, take 2h weapons.

€: i do not like the bound weapons since they tend to dissappear when i need them most and hava no magicka....

My main character is a Stormcloak battlemage. She uses primarily fire spells and switches to a fire-enchanted war axe in one hand when enemies close. I find dual wielding fiddly, so I just keep a spell in one hand and the melee weapon in the other. She gets enough defense from her smithing and enchanting skill.