I use Musicmatch Jukebox as my mp3 player on my comp and also to burn disks, it is excellent and I love it, converst files automatically and brusn it as an audio disk for reg CD players, can burn as MP3s for those devices that can play MP3s, etc.
Another good program is Nero for burning music CDs, it also does conversions and that if needs be. I really have not used Windows Media Player for burning CDs and playing music, but I willplay around with it and see if I can figure it out for you.