There are a couple of ways you can go about it. Music on a licensed CD is in .cda format. Windows Media Player can/does burn CDs with this format. (It's been a while since I've burned any, either way it plays in every player I've tried)

The other method I've used before, is to convert your mp3s to a .wav file and burn them to your CD with this format. Your CD player should be able to play it as well. Every player I've ever tried it on has worked.

There are a couple of programs that I've used for converting and they both work really well and rather quickly. They both do batch conversions, so you don't have to do them one at a time. You can get them here:

dBpowerAMP music converter (Freeware)
MPEG Suite (Freeware)

Give them a shot and see what you think. I've had great success with both methods.