Wish I had a mp3 player :-(
I bought one a couple of months ago and I love it. I got a Zen bottom-of-the-line (about $60) and I love it. Tiny and easy to use, and it has plenty of storage space for my purposes. I had to get better earpieces because I have small ears and the ones that came with it were uncomfortable, but otherwise I have no complaints.
If you want to use ITunes, you have to have an IPod, but if you just want to download MP3 files, a good clone will do.
If you have a CD player at home or in your car that won't play MP3's, you can convert the MP3 files into WAV format and then burn those files to the CD, which should then play on most CD players.
Many computer-based media players will have the ability to convert MP3 files to WAV, and you can also use standalone audio converters to do this.
If you do a search for "MP3 to WAV converter" you will get many hits, some of which will include freeware options.
Download iTunes from www.apple.com (either or Mac or PC) I believe it will allow you to import MP3s, and then you can burn the resulting playlist onto a music CD that can play in any regular CD player.