Investigate how each browser handles the playing of the music, and come up with a strategy so that when users click on "Play >>" the a track does actually play.
Store all your tracks in a relational database.
Store the album images as files on the file system, keep the address of that image in your relational database.
Carefully design your database so that you can store and retrieve the relationships between tracks, albums, artists, moods the various filters you see on the site you mentioned.
Have PHP then query your database to extract the various lists of tracks with a "Play >>" button next to them.
Give yourself a pat on the back.