I thought about a vampire start, but Skyrim's vampires are pretty well gimped and there's not a lot of places to make that work. Plus, if I'm reading right, vampires are actually a separate race and not just a diseased existing race. That would throw whole new wrinkles into things.
I'm not sure I see a problem. If you make it so you start at night (or in a vampire cave if it must start during the day), there isn't a risk of gimped stats at the start. Setting the player's race to the appropriate vampire race shouldn't be a problem, though there may be a bit more to it... you could look into the vampire scripts to see what needs to be done to properly change the player into a vampire.
I don't know enough about the werewolf part to even begin to touch that just yet.
Werewolves would be rather hard to do. It'd be a cool option, but the only form of lycanthropy the game allows the player to get is unique to the Companions, and they wouldn't give it to you until you've proven yourself. A "wild" werewolf start would need much more work than just setting up an alt start... lunar transformations and proper bloodlust, along with changes to the Ring of Hircine, and changes to various quests to deal with it all. Just adding "normal" werewolves would be a project in itself.