Damn Small Linux (DSL)
Puppy Linux
Xubuntu
Slackware
For your first objective (audio burning/editing), you could use even older hardware if you use a command-line sans GUI.
For your second, that depends on the games.
For three, I'd try something like Puppy or Slackware with XFCE.
By the way...the distros listed above are in no particular order.