m4p is an Advanced Audio Codec (AAC) format file. It uses Apple's FairPlay DRM to restrict how the file can be used. But this is generally viewed as a relatively loose form of DRM, with reasonable rights (multiple computers, iPods, CD burns). In terms of quality, it is a lossy format, so it is not perfect CD quality, but high enough that most people won't notice that big of a difference.
When you use iTunes to rip your own CD's, they are encoded is m4a, which is also AAC, but without the DRM. (You can chose what rate to rip at).
AAC is an open standard, FairPlay is proprietary, and many people are hoping that Apple will license it, so that songs purchased from iTMS can be played on other devices.
In terms of the song you bought. You can play it in iTunes, put it on your iPod, or burn it to a CD - convert it to an AIFF, which will play on just about every CD player. Once you convert it to AIIF, you can re-encode it as a MP3 if you wish, but that would probably degrade the quality further (kind of making a photocopy of a photocopy).
Apple was also introducing another format that was lossless, Apple Lossless Encoding, or something like that. It is CD quality, but it a slightly smaller size. I haven't checked them out - mainly because I've been pleased with the AAC's.
Interestingly, Sony recently introduced their new Network Walkman, in which they claimed to be able to store twice as many files as an iPod - what they downplay is that measurement is based on their ATRAK3 format at a low bitrate - Apples and Oranges so to speak.
Maybe Melanie needs a mini iPod for a present
