The term "MP3 player" encompasses a lot of things these days.
- Music only? Or do you want video? Wi-Fi? Games? Apps? Also, what types of digital files are you planning on using? For music, .mp3 files are the universal standard that virtually all device these days support. With .wma and .m4a (AAC, as Apple labels it) the choices get a bit more dicey as some devices won't support one or the other...or both. Use .flac or .ogg music codecs and the available choices get further narrowed.
- Sound quality? Subjective, but there ARE players that are generally seen as being better sounding than others.
- Style. Pretty? Cool? Aesthetics, size, weight, how it's designed to be carried, where it's going to be used, how it's going to be used, what activities do you plan on using your player with...all those things can matter.
- Durability and quality. Any player can break/be broken, but some are more rugged than others.
- Compatibility. PC, then you have a lot of choices. Mac, quite a few of those choices go away. Then there's the matter of accessories; not all players are equal in this regard. In fact, one player pretty much has most of the aftermarket to itself.
There are likely other things to think about as well (like budget), but these are at least the big ones.