For a first mage, I'd suggest a Breton, with the Mage birthsign.
Magic is very versatile in the game. It's possible (although challenging) to play a "pure mage," who uses no weapons at all.
As for armor, it's a personal preference, but you should be aware that wearing armor reduces your spell effectiveness. It's not too big of a problem for some magic skills, like Destruction or Restoration, but it will be a big deal for Illusion magic later in the game. Armor is not actually a Battlemage skill, though; that would be more like Oblivion's default Spellsword or Sorcerer.
I rather like the default Battlemage, but I'd suggest that you create a custom class version of it, substituting Restoration for the Blunt skill, so you'd have:
Alchemy, Alteration, Blade, Restoration, Conjuration, Destruction, Mysticism for major skills.
I think I'd go with Intelligence and Endurance for favored attributes.
I'd equip the character with a good dagger (you can pick a silver one up from several mages guild halls, once you join), and I'd use it in conjunction with Alchemy (poison) for when an enemy manages to charge you. Your character can wear heavy armor, which will train up and give you advances in Endurance (better health) as you level up.