Yes, a zip should work just fine. :-) There are two disk capacities I know of: 100 MB and 250 MB. Even the 100 MB are perfectly acceptable. Since your average higher fidelity MP3 is about 5 MBs, you could fit nearly 20 songs on one disk at a time.

A note about zip compression:
MP3s are already compressed using the Mpeg Layer 3 format. You will not gain more than 1 or 2 % of space by compressing the songs into a zip archive. Movie downloads are also compressed (one would hope!), so they won't need zipping either. Most other downloads, such as Jpeg images and executable program installations, can benefit to some degree from file compression, though they are already set to go in a slightly lower compression ratio.