Pretty games- Do not really care. I play many older games and games with little graphical effort put in them. Though yes I do find it nice.
Music- Music can hamper my enjoyment some. If it is really annoying music that is.
Gameplay- This is the biggest thing that matters to me. IF there is bad gameplay but the rest is good I still will not play it for very long if at all.
Story- Unless it is a JRPG I could care less about the story. I can enjoy the quirky ones just as much as the serious ones if not more.