I bought Miss C a new mp3 player for Christmas. I was only after something small and relatively cheap so following a bit of research I went for a Sansa Clip+. As the player features a memory card slot, rather than choose one of the models with a larger amount of storage I went for the smallest 2GB model and then bought a generic 8GB MicroSD card to go with it.
Seems to be a great little player. Small, solid, easy to navigate, OK sound quality and with the addition of the MicroSD card I got a 10GB player for just over thirty quid. Miss C seems to like it too. So if you are after a compact and low cost mp3 player for your casual listening needs you could do worse than to take a look at the Clip+.