The mulligan rule is by far, IMHO, the most needed feature for the game. Especially as tournaments become a bigger part of the community. Mulligans reduce luck-based wins and losses, give another advantage to skilled players, and will stop a lot of griping. While I think some of the other options are needed, this is a change to the fundamental way the game is played that I think is essential. I also think that with the way the game works, one free mulligan would be a good thing, but that's something that needs to be worked out through testing.
(I also think the way that you can sub in a whole deck in tournaments is a bit preposterous, but perhaps that's letting my MTG background get the best of me)