I was wondering if I could get a little help on how to make a balanced Battlemage.

Any thoughts and/or suggestions would be appreciated.

I tend to favor the Oblivion Battlemage class - one handed weapons, destruction, conjuration, alteration, no armor. Very fun class, IMO.
If you want armor, however, I'd go for heavy armor.

Take the respite perk in with a few more from restoration. No need to take stamina at level up ever. Necromage and recovery are pretty useful, too.
Your perks will be spread through magic and combat, so I would suggest picking one destruction element to perk for damage and leaving it at that.
If you are going unarmoured, no armour and melee is one of the most challenging things you can do in this game, make sure to take the mage armour perks, could be the difference between life and death.

if you dont rely on conjuration get the atronach stone

heavy armor, one handed, magic skills you enjoy

put points into magicka and health, if you cant cast enough spells put points into magicka, if your dieing put points into health. Don't really know the ratio you'd want, depends if you like magick or swordplay more.

Basically this is the perfect set up for a strait battle mage, lob fire blasts til they get close then finish them with your weapon. I personally like summons as they act as meat shields or long range attackers (atronachs) Heavy armor means you don't have to waste your magicka on shield spells. Restoration can be used for wards and healing you, both are very useful.

I did the same with a character of mine but used light armor, i never really got attacked because of my summons and follower, i used bound sword as it fit the mage feel. Its pretty fun really

I'm a little confused, I thought battlemages were magic only with heavy armor and spellswords were one-handed w/ magic, maybe it's a matter of semantics. I just started an Altmer spellsword, gonna try destruction (fire only), illusion, conjuration, alchemy, enchanting and maybe restoration if things get too tough. He's gonna wear heavy boots and gauntlets w/ enchanted robes. We'll see what happens...

I think in a fantasy game with no real class structure it can be however you want it...and i guess your right about the spell sword thing. I'd also say its all about the look your trying to go for