And I start Dawnguard?

In order to begin Dawnguard's Main Quest, you have to initally join the Dawnguard. I haven't tested this myself, but I don't see them letting a vampire into their ranks, so you'd most likely have to be cured first, then become a Vampire Lord after the first quest, though I may be wrong.

Become a Vampire Lord after the first quest? You get to choose between the Dawnguard and Vampires right away?

Yeah, you meet Serana in the first dungeon you're sent to by the Dawnguard, and she asks you to take her to Castle Volkihar. There you are allowed to choose between the Dawnguard and the Volkihar.

Thanks for the info

When you choose the Dawnguard, you're sent to do a quest to recruit two guys to help out. After getting them both, Isran shines light on all three of you and they'll figure out you're a vampire and direct you to Morthal for a cure. Until that point, you can be a vampire doing the Dawnguard as much as you want.

Yes, you get different dialogue when you are already a vampire.