The Argonians make really good vampires actually, Histskin (their racial power) becomes a lot more helpful when you can't regenerate health naturally.
Alternatively, if your vampire has some skill in restoration, playing as an Altmer is possible. Using the Highborn power will cause your magicka to regenerate, which you can use for both healing and offensive magic.
Speaking from experience, since one of my characters is an Altmer vampire. To be honest, I don't notice a huge amount of advantages to being a vampire in the vanilla game, and I was going to cure her up until the point when I heard about the vampire lord in Dawnguard. So, basically, she's going to join the Vampires and end the tyranny of the sun, as they put it, because taking the "evil" road is always more fun. ^^
My primary character is my Imperial paladin. Heavy armour, one handed, block and restoration. He's a fairly old character, and was always one to hunt the undead. The Dawnguard is perfect for him. Sure, I don't think I'll give him a crossbow, since that's not suiting to his play style, but I'm sure a sharp blade will work just as well.
And of course I plan on making a third character. Argonian probably. Sure, he's not going to join either side of the war, but he'll know how to fire a crossbow better than any of them.