So these are my current skills: One-Handed, Restoration, Alteration, Enchanting, Smithing, Conjuration, Heavy Armor, and Destruction or Archery

Basically, should I use Destruction or Archery? Here's what I have

Destruction Pros - Magic based so no need to carry around more items

Destruction Cons - Needs to take up enchantment slots to be viable at higher levels

Archery Pros - Powerful if leveled up, and can be enchanted to deal more damage

Archery Cons - Need to get arrows and carry around a bow.

Basically, I've already got other Magic Schools so I'm already Spell Based Warrior class, but should I go the more traditional route with destruction or go archery?

So any help?

I would go with archery, with you already using conjuration, restoration and alteration your magika reserves are going to be pretty taxed. Using archery also frees up those enchantment slots you were worrying about. Arrows are also pretty cheap and common to come by so that isn't a problem.

Battle mage makes me say Destruction. I'm also rather fond of throwing fireballs at people.

And it also goes hand in hand with the one handed skill.

If you're already using Conjuration, use bound bow for archery; no inventory, free arrows and medium high damage with no smithing.

I use both.Archery and fire are my 2 favorite things.