I didn't think so, but answers to this question have left me curious. Is an enchantment on a Gold Emerald Ring more powerful than one placed on a plain Silver Ring? Does a fancy bejeweled circlet have more magickal potential than a run of the mill hat? Do Fine Boots get a better modifier than shoes?
After some experimentation, it seems the item itself (unlike in Morrowind) does not affect the quality of the effects you enchant it with. So Fine Boots of Fortify Carry Weight will have the same amount of weight increase as Boots of Fortify Carry Weight, assuming everything else is the same.
What it does affect, however, is the price. It seems that enchanting affects the price of the item by a percentage - thus, a value 500 ring may increase to 1000, where a 300 value ring may only increase to 600. I'm not sure whether or not this value increase is linear, but I have definitely noticed a difference.
No it is not, it is instead affected by your enchantment level and perks unlocked. The price will vary though...