If you are rolling a vampire (dawnguard) what is the best weapon to use for a vampire?

One handed? Bow and Arrow? Other?

Vampires don't really get any "best weapons", its still anything you can craft.

Best you can have is a sword at the end of the Dawnguard MQ.

Well what I mean is, what weapon should I use as a vampire. i will mostly be using magic, but is bound weapon just the best way to go?

Depends on what type of character and personality your vamp has. My mage vamps use either no weapon or bound sword. Mostly, since they are mages, use only destruction magic. For you, it will depend on what YOU feel is right for your character.

daedric sword

Im a Vampire Lord and I mainly use Destruction Spells and the Slay Living from Restoration.

However, I've picked up one of the Dawnguard Axe's from a one of their corpses. It has a good bonus against other Vampires (should I need it) and has a decent Base Damage.

It depends on your character. If you are more rogue-like, Auriel's Bow is pretty cool. If you like One-Handed, Harkon's Sword is also a very viable option, but both weapons you will only get way later in the dlc's MQ. What I like the most about both weapons is that they are Unique, and the enchantments they have are very useful.