How can I unlock more songs in Theatrhythm: Final Fantasy?

Starting at 10,000 rhythmia, and every 5,000rm after that, you get a new song. There is one exception: you get Battle 1 (FFVI) at 27,500rm.

As for farming rhythmia, I find playing ultimate scores seems to work the best. I currently have 31000, and playing awakening (FFXI BMS) nets you ~ 175 rhythmia per play. I was playing without shantotto in my team, so you're looking at 200+ per play. Having a team full of males/females helps slightly, too, giving you +10 rhythmia.

You start unlocking chaos shrine scores at 27500 rhythmia. For these ones, new songs seem to be unlocked every 2500 points, instead.