You're best off buying an iPod Mini for its value if you want something 1GB or higher, but that might still be too expensive, but if you're looking for a cheap MP3 player the next cheapest thing is a flash memory based player, which you might as well get if it's for jogging. 128MB of flash will get you enough music, and you can quickly upload music before you leave, especially if you make playlists that you can use to shift over groups of songs.

This one is pretty sweet. $149 US and has a voice recorder, FM tuner + recorder, plays MP3/OGG/WMA, and you can also use it as a portable storage device. It has 256MB of storage.