I have 3 characters and one of them have completed the dawnguard questline.
Now i want to make a vampire play through with one of my other 2 characters.
This may sound nerdy. But i want to see wich of my characters would suit the vamp quests the best.

I have a wood elf. Sneaky archer assassin who i don't really respect the law with. Play by my own rules etc.
And i have a mage. Very good in all the schools of magic and arch mage of winterhold. He is kind of neutral on the entire "being good or evil".

Who would have the most benefits by joining the vamps. And who would be best from a role playing standpoint?

Sneaky characters who don't respect the law and play by their own rules are excellent vampire material.

Mages who don't really care about much except magic? Not so much.

Thanks then. I guess my wood elf and i have a new adventure to embark on. Plus it will not hurt to get him Auriels bow and those "serana" arrows

The crossbow upgrades might be fun for your archer though. If you want them, you'll have to join the Dawnguard. Very powerful in the end.

I vote the Woodelf archer as well, but there's nothing wrong with a neutral character being a Vampire as well. You can still play the questline in a neutral, non-evil way.

The only thing about my wood elf is that he has no magicka or magic abilities. Will that be needed?

You get some great advantages to being a Vampire including a boost to Illusion spells, but playing as a sneaky archer as a Vampire will work fine if you don't want to level up any magic schools. As a Vampire Lord you will get extra Magicka as well as 10% extra Magicka regeneration, so you can use that to power the magic based VL abilities, which are self contained.
You may want to level up Restoration in order to take the Necromage perk. A Necromage Vampire can become a very powerful character.

My wood elf vampire uses a lot of magic and bound bow for archery and that character is extremely fun to play as. I would strongly recommend it.

I'd vote mage since the Vampire Lord is a heavy magic user. You could do the sneaky archer, but you'd have to rely more
on NOT transforming into a Vampire Lord and just remain a regular vampire, and there's no fun in that if you ask me.

But transforming into a Vampire Lord is self contained, with no access to any spells outside of it. Once transformed you get extra magicka and regen and VL specific abilities, including Blood Magic (or something - I don't actually use the VL for anything), so you could probably be any class as a VL and then level up whatever VL abilities you want. Or you could also just use the melee VL abilities.