I am sure someone knows more about this than me, but as no one else has answered I will have a go.
All 3 formats are compression formats, where the music is compressed to reduce the file size (and hence sound quality) although many may not notice the difference.
WAV was first I think, but the file sizes are still quite large so it is not popular with people on the internet due to time it takes to download a file.
MP3 was next and these files are very small, hence the popularity on the internet. I think this is pretty open standard.
Microsoft then developed WMA which I think are smaller than MP3 but not sure by how much.
I think all devices will support mp3.
Many will support WMA (and of course Windows Media Player supports it because Microsoft wrote both)
Not sure about WAV, but my GUESS (no more than that) is that most devices like mp3 players will not support it (but willing to be proved wrong)
If you stick with mp3 files you cant got wrong, but many devices now also support WMA.