For synthesized music midi’s are common among ameteurs, and modules among professionals or ameteurs who want to be pros
For recorded music MP3 is the most common format.
Midis (.mid) store simply “Piano plays C# for 2 beats starting at this time…” etc, so are quite small, but generally not very high quality, and the sound changes from computer to computer, depending on how that sound card defines a “piano” sound. However it is very widely supported.
Modules (.mod, .xm, .s3m, .it are among the more common formats) store the music similar to a mid, but also store the “samples”, ie exactly what a piano sounds like. Because of this you can get higher quality, and still have a relatively small file. However they’re not as widely supported. Most high-end audioplaying software, like winamp can play them, but you can’t embed them in webpages for example.
Sampled formats (either compressed or not, .wav, .mp3, .ogg, etc) store exactly the sound that needs to be played. These are, by nature, much larger than synthesized music, but allow much more freedom in the sound. In particular, you can record actual people on actual instruments playing the music.
They also let you put other sounds, like lyrics, over the top. This is downright impossible in midis, and while possible in modules it is rather pointless unless the lyrics are very repedative, eg a lot of techno music.
It all depends on what you’re using it for (the right tool for the right job…)
Incidentally, if you want to import the music into blender, it needs to be in .wav format (but can be compressed, iirc) - midis and modules don’t cut it, but you can compress a .wav with the mp3 codec (this is not the same as a .mp3 file, but a .wav file with compressed data - just like a compressed .avi is different to a .mpg for example).