Indeed you can. I would personally go with the sandisk Sansa Clip, or then Sandisk's higher-end mp3 players. It's worth checking out.
True, I currently have one of the Sansa familly (although mine is old) and am very pleased with it. It still works after all it went through.
You can't go wrong with an IPod, but they can be a bit expensive.
Yes, you can go wrong with an Ipod, depends what you do with it.