There are lots of places to discover music you might like, especially tracks you'll never have heard before. Building mixes is fairly easy using the likes of Spotify which can then be Paused/Played or skipped using a single switch.
8tracks.com - Create music mixes up to about 30 minutes.
Last.FM - Very simple search site - with a huge range to choose from.
MySpace Music - Many bands and artists have some free tracks to listen to.
Sound Cloud - Much non-commercial music.
Spotify - Perhaps the best of all, but with limited access around the world.
The Hype Machine - Lots of unusual and rare tracks.
We7 - Fair range of streaming music.
YouTube - Staggeringly huge range of music videos to track down.
See also the OneSwitch.org.uk Switch Accessible Music area for more switch music ideas and this great Free Music for Videos post [updated June 2015].