Does your smithing skill when you CREATE a new piece of armor or weapon effect the Damage or Armor Rating? I know it can with the improving but I was wondering if the base item would be better just because your smithing skill was higher?

I think that the base stats are the same regardless of your skill, and that improving and enchanting them is the only way to buff it up. Additional perks in the armour and weapon skill trees will also boost the damage. Don't quote me on it though, I don't actually own the game.

No directly, as your smithing skill has no bearing on the base damage/Armour rating of the item you make, just which Items can be made.

But it does have a bearing on the improvement of items as the higher the skill the higher you can improve them which does have an effect on their damage/Armour rating

Thank you guys, that is what I suspected.