Actually, I have the Sansa clip plus and you can set it to play a single playlist continuously. I don't really like the navigation features (it's not intuitive for me), but overall, I'm happy with it. It was inexpensive, it's very light and small, and it works well.

I LOVED my old Rio Forge Sport that totally met all of your requirements, but they don't make it anymore. I lost mine and I was looking for another one when I found the Clip. The Rio used AAA batteries, had playlists, was small and durable and it had room for an SD card to expand the memory. Mine currently has a 2GB card in it (that again, I wish I could find!) that I never even came close to filling up.