Yeah, one of you hosts the lobby but that doesn't mean you're hosting the game. You make a lobby, invite your friends to the lobby then press go and it finds a server for you.
But yeah, it'll be L4D2 we'll be playing. It's better than 1 and also contains all of 1's content so 1 is pretty much redundant.
Add
me on Steam, I think I already have Graphitone and Chrisssssss as friends.