If you're going the iPod route, you might want to consider the iPod Classic for $50 more than the 8GB Nano. I realize it's over your budget, but it is cheaper per GB.

The Creative Zen is a very good iPod alternative. And you can get the 8GB version on Amazon for $120. The 16GB is under $200. It also takes SD cards so you can expand the memory. Amazon.com's mp3 downloads store and Amazon Unbox are great alternatives to iTunes store, provided that you're in the United States. Amazon is planning to roll these out in other countries, but I'm not sure of the timeline on this.

Creative Zen player:
http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Daps&field-keywords=creative+zen

Amazon Unbox:
http://www.amazon.com/b/?&node=16261631

Amazon mp3 downloads:
http://www.amazon.com/MP3-Music-Download/b/ref=sa_menu_dmusic1?ie=UTF8&node=163856011