Here is a list of songs for you to use as background music in games. Almost none of them are by me; just collected by me. Check the sizes -- the larger the song, the longer it will take to download when used ingame! MIDIs are much smaller but are more like sheet music; AIFFs are more like MP3s or WAVs.
Will this ruin our game in any way?
If you add any new textures or other online content to the game after first adding the music, (for example, your character's skin when joining the game) they probably won't load until the song is done loading, which can take a while, anywhere from a few seconds to about a minute depending on the size and internet connection.