If you already have the game, don't pay twice for it. You can add your existing copy in your Steam library manually (iirc; though I don't remember how it is done) if you want it there. And just make your own recommendation to your brother. If you like New Vegas better, recommend that to him. Fallout 3 might feel a bit more simple than it already is after New Vegas, but it shouldn't matter.
Fallout 3 first then Fallout: New Vegas, playing Fallout 3 second would seem like an anticlimix imo with the inferior story, characters and writing.
You should play fallout 1 and 2 if you haven't they are also fantastic games