There's two things to consider when running a Pop'n tournament:
-What songs get played
-How you determine who wins a given bracket
For songs to be played, the important thing is that two songs are played by each player during a given round. Now you can either let each player choose a song and then each plays both; or have a set list of songs for the players to play as determined by round or individual bracket. (In the second case, a "here's four songs, which ones don't you guys want to play" system works fairly well.) Either of these systems allows a bit of player choice so someone doesn't get screwed on something they for whatever reason can't play or can't pass without having some say in it.
As for who wins, you can do one of two things: Count the score on each song and have per song victories, then whoever wins both or one and a tiebreaker wins the round; or you can total up the points between the two songs and use that (which wouldn't normally need a tiebreaker). Failing the song makes it only count for half, and in the event of a tie on a given song (or in the point based system overall), combo determines the victor.
So if you have more casual first time players, let them pick and base it per song, with a tiebreaker set by you for each round. This is how it was done at Otakon with quite a bit of success, and it was a lot of fun.
More pro players? Go by score, use the pick two system. This is how it was done at Bowl-Manifest 2006, with intense competition and a nervewracking 677 point victory at the end.
Either one's a hell of a lot of fun.
So I'm going to run a Pop'n Music tournament... 
