Turns out I have some time on my hands.
Firstly, I want to say that I've played an Imperial Battlemage in Skyrim, and it was awesome. Here's how the build went:
General skills were Alteration, Restoration and One Handed. I barely dabbled in Conjuration, picking three perks for the Bound Sword (Novice Conjuration, Mystic Binding, and the Soul Trap perk).
Typically, I'd go into battle with an armor spell in my left hand and the Bound Sword spell in my right, casting both to start with and then switching my left hand to the hotkeyed Restoration spell I'd use to heal (usually Fast Healing). It was a whole lot of fun, and I was able to switch back and forth between armor spells and healing on the fly. No physical armor meant free, easy movement, and mobility is important when using a single weapon. Wards for dragon breath and enemy mages, shouts, and Dawnbreaker just made everything so much fun.
I got into Enchanting because I ended up with more souls than I knew what to do with. It was a useful skill, since being a Battlemage means I need to spread myself thin over all three attributes and enchanted equipment can help mitigate any disadvantage you'd normally have. The Gauldur Amulet and Master Robes of Restoration were great, as well (I used Restoration robes over others or crafted clothing because it was the spell type I'd cast most often, since armor and conjured weapons stay up for a while, and you can't make a bonus that great on your own).
What with all that goodness, I eventually got into using Paralyze and dove into Smithing...I highly advise avoiding both. Shouts already have a means for circumventing Paralyze (namely, Fus Ro Dah and Ice Form). It's also expensive to cast (and a Battlemage doesn't have a lot of magicka), and generally you'd need only either an armor spell or paralysis in a battle, but not both, so it was a lot less fun. As for Smithing, I was already very competent and powerful in battle, and Smithing just broke it for me. Instead of using and appreciating my Bound Sword and any one-handed weapon I found or enchanted, it was down to Deadric weapons, and I didn't even use armor, so it felt like a terrible waste

Smithing was when the character stopped being fun.
Recently, I made a Breton Battlemage, but he's no fun either. Destruction, Heavy Armor, One Handed, Restoration, Enchanting--basically what you want--and it's a drag. But I have a better idea: instead of focusing on Restoration, use Alchemy. You already have enough skills to use in combat (One Handed and Destruction--two is more than enough), and you only have two hands, so it's good to be a little more focused. Again, don't smith. Here's the build idea:
Main skills:
-One Handed
-Destruction
-Heavy Armor
Supplemented by:
-Alchemy
-Enchanting
Again, with Enchanting, you can mitigate the fact that you have to spread yourself thin stat-wise. With Enchanting, you can give your blades a burning edge or can "daze" (slow/stamina drain) enemies with a mace, which, personally, I find quite Battlemagey.
With Alchemy, you can restore all three of your attributes (where Restoration would be draining your magicka reserves
more, which is bad since you need Destruction spells), or boost Destruction/One Handed damage when necessary, but that's not what I like most about this build. What's better is that you can increase your defenses greatly (magic/elemental resistance, Heavy Armor skill) for that Battlemage feel (or, at least, that's how I feel--after playing KoA: Reckoning, I find Battlemages defensive). And instead of boosting Destruction or One Handed damage, you can poison your enemies so that your shock spells and shock damage enhanced sword deal more damage. The weakness to element poisons are stronger than the One Handed/Destruction buffs you can get, as well as apply to damage dealt by companions, summons (summoned via scrolls/staves, of course) or other attacking enemies.
I'd go for a Breton with the Lord, Lover, Serpent or Atronach stones. Any of those would synergize wonderfully, but avoid the Lord stone if you have magic resistance on your equipment (Atronach is still a good stone even with such equipment). But if you want Imperial, so be it; I still advise the same skills and stones.
I hope that helped
