If not, then you would have to convert them. There is third party software that should do this. Check download.com(CNET's site) first and search for "AAC to mp3 conversion" - you should be able to find something.
If you have purchased iTunes music (you said you didn't, but this is to answer hambla's question too) - you would need to burn them as an audio cd and then rerip them onto your computer as mp3s.
If they are all mp3's - no problem. You can use windows media player (or other software) to manage your music in your iTunes library. You would just need to have it find your music. In WMP, go to "file", then "add to library", then by "searching computer". It might be different in WMP 11, but the process should be similar.
Most current hard drive based players come in 30GB, 60GB, or more. Almost all of them have video (If you don't want to use it, you don't need to, but viewing pictures is a nice option) You might want to go with something that's 30GB. If your new player supports it, you could always use the extra space for back up storage.
Sorry, I'm an iPod person. I can name a few players, but I don't know from experience what they're like. Give it time, you might get some responses from the non-iPod loving community.
Creative Zen Vision:M
Microsoft Zune - but you're stuck using their software, much like iPod +iTunes
Toshiba Gigabeat S