i dont see why you would want to go with a cd player that plays mp3s unless you are really worried about losing something vaulable or hurting an expensive player on the trail..
There are tons of very very cheap mp3 players that will let you do what you want. Get a flash one becuase yes you are not suppose to run with the hard drive ones...even tho a lot of people do. I would look for a flash one that lets you use memory sticks like SD or something...those are real nice cause they are easy to use, dont really have any closed media format and let you upgrade/downgrade your size if u dont like what u have.
You can get some for real cheap.