If you go to the file menu and select "exit," Spotify will completely shut down (and all music should stop).
I really don't know how to stop it from playing the next track when you have it open. If you play a song from an album list or playlist, it will automatically play the next track when it finishes. I guess if you want it to stop, you can just press stop in the transport control. It does seem annoying that there isn't a preference setting to play one track at a time. I did a Google search for this issue and the only results I found were people complaining that their Spotify
isn't playing the next track automatically. Annoying people!