i was wondering what would be the best choice (or any choice) for an mp3 player to play songs on a website, where the visitor can choose which of the available songs to play.

I really don't know much about this, so all I can really think of is a flash player. They are big, but they are functional on many sites. You might be able to find something on this at www.flashkit.com or www.pixel2life.com

Also, you can also use a regular embedded multimedia player (WMP, Quiktime, Real, etc) and have a drop down menu for chosing the song, but IMO, those are a bit bulky and unattractive.