I don't know of any specific distributions for this...
I'd start off installing something very minimal. If you know what you are doing then debian would be good. If your less confident DSL Linux
is aimed at lower spec computers and you can run scripts on it to install it to hard disk.
I'd reccommend a small windowmanager my personal preference would be fluxbox
if your adventurous.
I'd then suggest a light weight media player. xmms is good as it is light weight and has a very flexible playlist with jump to track and other options.
This will run fast and reliably, you can even script xmms to load with fluxbox or oroborus if the machine is for one purpose.
If you want to get more adventurous you may have to play arround with other media players.
You may be able to run without a window manager at all, I did this for a 133 that i set up to only be a remote terminal client for a MS server (the only thing that loaded with X was the rdesktop application with the commands to connect to (but not log into) the MS server).