Here's how things work. In Arcade mode, you get to choose from three songs. With each song you pass, the selection because larger and more varied (read as: difficult). Then, after the third song, you're back at square one.
Each time you play a song, you unlock it in Free (or something like that) mode. Therefore, you may want to start keeping track of the songs you have/haven't played if you want to unlock them all. It's a lot like the way Samba de Amigo handled its arcade mode, if you're familiar with that.
As for the song colors, I think it has something to do with where they came from, other Arika games, Namco games, or "original" songs.
If you're hung up on the gameplay mechanics, the manual and the training mode do a nice job of explaining things. Don't even ask me about the "you just beat three songs in arcade mode" mini-game, I still haven't figured out the controls there.