I had a cheap Alba MP3 player from Argos that you could just copy standard music files to. It was alright if you didn't mind the randomness of the tracks it played out, sounded okay with a decent pair of headphones to replace the tinny ones you got with it.
Didn't want an expensive one as I bought it for putting on when walking the moors when the wind whistling around my head got annoying!
It just stopped working one day though and I'm looking for another.