In the main mode which is all about score and the characters may as well not even be there. I find this mode quite boring and not really what the game should have focused on.

The Chaos Shrine is a different beast however. This is where you want to equip skills and items as score is not important at all. Here you want to have your party leader with a high Agility score so you can pass the boss sign in the field stage so you can encounter boss 2 or 3 in the battle stage. Then you want good skills so you can kill as many enemies as possible so you can kill the boss (possibly multiple times) before the song ends so you can get good items/shards. Also killing more give you more exp which is required to get more difficult dark notes which generally have better items available in them.

Every time you beat the number 1 chaos note in your list you will unlock a new note which will have a difficulty score that is the average of your parties level. So replaying darks notes over is quite useful so that you can both get shards to unlock characters but it will also level up your characters so when you play the note that will unlock a new one the next note will be of a much higher level.