I was wondering what the best one-handed ax in the game is?(may be an opinionated question)
Also is there any certain elemental damage to enchant on an ax better or more advantagous than an other? (i play on xbox and completely realize this is probably the 900th time such a question has been asked but i am a newbie and find it hard not ask a question like this when i know the knowledge pool that is here)

Disregarding weight, the Daedric War Axe is worth a look. It drops randomly off of all Dremora, and Menta Na.

The only sure way to get it is off of Gordol in Ashalmawia -- he attacks on sight, and House Redoran wants him dead, anyways.

The Daedric is best for brute damage. The Stalhrim War Axe takes more enchantment and is powerful even in it's unenchanted form. Ebony and Nordic Silver are nice too. I suggest you get at least one of each.
Stalhrim and Nordic Silver are added with the Bloodmoon expansion.

I think a cast on strike absorb health on touch XX points for one second is the most powerful enchantment for a weapon. It sucks health from your opponent, gives the health to you, and can't be reflected. Set the XX as high as the axe will take. Use a good soulgem and soul to get a good number of enchanted hits before the weapon's charge is exhausted.

Indeed, once you have this enchantment, you're a lot more powerful. I also reccomend a combo of Absorb health and Fatigue, which means that your attacks will always be at their best and you will lose little health, if any.