I am assuming you mean an mp3 player? I can't speak outside of the iPod world but I would recommend an iPod Nano. The full size iPod Videos aren't meant for that type of jostling and will turn themselves off mid-run. The Shuffles don't hold up well to sweat or moisture and as DBF recently experienced, will die after about three months if exposed to those elements a lot. (Apple is going to replace it, but this is pretty common from what I've been reading on the internet).
I love my 3rd gen Nano; it fits in my running short/skirt pockets perfectly. The new 4th gen Nano is larger so there may be some trouble there but it's still a good player. Plus, you can get the Nike+ adapter to log your mileage.