hmmm.... I don't have a separate MP3 player yet, but I really do like my new phone. I just wish I could figure out how to use a song I upload to it myself as a ringtone.
Don't buy an iPod, they're the most overpriced crapfests ever created. Creative HD mp3's are very well-made, but cheaper models like 1-2GB SanDisks and Sony's work just as well. I have a 512MB Sony that hasn't given me a single problem since the day I got it, and the software supplied with it converts music to a neat little format that takes up about half as much space as mp3, so I get the same effect as about a 1GB player.
If you're looking for something up past the 2GB line, I'd say buy a Creative HD mp3, as from what I've heard they're very reliable, but if you're wanting to keep the price range around 100-150, stick with a Sony or a Sandisk 2GB.
I got a 512MB RCA Lyra with an SD card slot for $63
Just like I planned from the start... well, either that or a Dell DJ, but I couldn't find those anywhere and they probably cost more.