The way we've always done it is to pick Round 1, then after re-seeding complete the bracket. Personally, I think it's way too easy if you only have to pick a 1 out of 4 rather than a 1 out of 8.
The scoring was like this:
R1 - 1 point for series winner, bonus 1 for games
R2 - 2 points for winner, 1 for games
R3 - 3 points for winner, 1 for games
Final - 4 points for winner, 1 for games