Made a battlemage type character but not I'm sure what skills to focus on most. So far I think it will be one handed, heavy armour, destruction, restoration, alteration. I'm very unfamiliar with magic builds; I put hundreds of hours into Oblivion and Morrowind and never ever made a mage. Are there any skills that I will find very beneficial that I have missed? I read on here that enchanting is super-amazing but I don't even know how the levelling works for it.

Try destruction, the fire or ice cloak should come in handy for a battle mage.

Alternation is good if you seek for a more protective style

wards from restoration give you nice protection from those pesky caster

Enchanting is way too powerful imo lol.

Enchanting will let you to juice up any plain armor or weapons. So if you find a nice mace, you can enchant it to do extra damage. Or you could use enchantment to make your armor resistant to fire or magic. If you don't like companions, you might try conjuration so you have a distraction for any attackers. Restoration is a must have so you can heal yourself instead of using potions.

I'm going with One-Handed weapons, Destruction, Restoration, and Heavy Armor as my mainstays.

I'm going with One-Handed Weapons, Conjuration, Destruction, Heavy Armour and, something else, I haven't decided yet. EIther Restoration or Alteration.

I'm only level 9 but currently I'm having fun with:

Destruction (All trees)
Enchanting
One-Handed (Axe tree)
Heavy Armor
Smithing

I typically open with one or two dual spells from range (single or combined), pull out the axe at about mid range while firing destruction from the other hand, and then fully switch to warding/healing with magic and power attacks with the axe.
I'm not planning my build point by point so I may add a bit of Alteration and the Mace tree of one-handed as I go.

Im using, 1h, restoration, destruction, enchanting and heavy armour.

not sure whether to bother with conjuration :/

level 15, build works well!

The best "Battlemage" focuses almost exclusively on Conjuration. Bound weapons and a Dremora. Nothing else is needed, and nothing else comes remotely close for Mages in this game. Destruction takes around four or five times as long to kill things with and your entire mana pool.

This. Basic warrior skills are brutal - especially when enhanced with enchanting and smithing. As is conjuration.