Right now my character is using a dagger (silver I think) which has the 'does +30 shock damage on hit'. It just sucks down the Soul Gems to recharge it.. but I can take out most things with 2 or 3 swipes.
Even when I'm in the Oblivion gates, and taking on 3 or 4 demons at a time.. I just chew through them with the little dagger.
Plus.. one of my primary spells is a 'Heal 25 points'. I also keep a large collection of Healing potions for times when mana runs low.
As for my offensive spells, I have both fire and ice damage, usually I've found someone resistant to one is vulerable to the other.
I don't think I could do an archer.. as I said before..I'm the fighter/battle mage combo.. my weakness is mostly anything thivery.. sneak - open locks, etc