The audio data contained on a retail audio-CD is not stored in the Mp3 or WAVE formats and therefore those formats won't be able to be played back by a standalone player.
You'll notice that if you ever try to access a disc to play it on your computer the file will be a ".cda" file. You'll need to select to burn an audio disc specifically using an application designed for it and whatever processes the files will convert them to the format necessary for your CD player to play them.
It's slightly bizarre that you know what a "stand alone" CD player is but not that information.
Feel free to post back if you need anymore help.
EDIT: Hmm, fifteenth of August. I doubt he'll come back.