Preferably a battlemage. But I like to play realistically in a sense where a race would wear an armor that suits them, or use weapons that suit them. Not a wood elf wearing orcish armor wielding a battle axe. Can anyone suggest what I'm looking for? I keep restarting cause I can't figure it out.

Part of the problem may be that there isn't any "right" or "realistic" combination of race/armor/weapons/skills in the Elder Scrolls lore. Certain races have certain skill advantages, but they're slight. Taking your example of a heavily armed and armored Bosmer, in a previous game (Morrowind) there was a Bosmer in Ebony armor (Gaenor) who was one of the toughest enemies in the game. In Oblivion, again we faced an Ebony-clad Bosmer, this one a female, who wielded Umbra, one of the most powerful swords in the game. It didn't come across as "unrealistic" to me; those elves were dangerous.

But for a battlemage, and trying to stick to the racial preferences, I'd make three suggestions.

1. High Elf in light armor, concentrating on Illusion and Destruction as primary magical skills, and wielding a staff as a weapon (when not dual-casting,)

2. Breton in heavy armor, using Conjuration as a main skill, along with Restoration, and using a bow as a weapon, possibly poisoned; your character could become a master of Alchemy.

3. Dark Elf in light armor, mastering Destruction; Dunmers are good at just about everything, and could be a sneaky mage type.

On the other hand, I like to play against type, so one of my favorite characters is an Orc Sorcerer; she wears heavy armor, and uses Conjuration and a crossbow.

Redguard and Breton make the best Battlmages. If you want to be more combat go Redguard if you want more defense go Breton. But you also want to be realstic so Redguard might not be the best since their armor svcks.

High Elfs make the best pure mage and you give them elven armor or a robe.

So would you recommend ebony armor for the Breton?

I think Ebony armor is among the best-looking armor in the game. Something to work towards.

Check out 'The Evoker' on the tamrielvault. It's a pure destruction mage that doesn't svck.

I loved my necro Breton.
Light armor, conjured sword, necromancy, illusion for enraging enemies, muffle and invisibillity.

The first kill was either a stealth kill or by enraging enemies.
Then the risen dead would help me decimate the foes until I would step in with my conjured sword to finish the rest.

Loved that character.