Most of the theme music to the films, were well known (This is because either a) They production company got rights to the music, or b) the music artist gave the production company the music to boost publicity). We knew that we were unable to use Copyrighted music in our short film, so we had to carefully search for Royalty Free music which was appropriate!
Most of the music on the films we found, was soft rock; included guitars, and didn't always start singing immediatley.
Out of many Royalty Free music websites we found, a site called DanoSongs.com had a very wide range of music for us to search through.
After careful consideration, we found two songs that we liked (One of which is the one we used for the actual film)
http://www.danosongs.com/music/danosongs.com-crawledoutofagrave.mp3 - This introduction was similiar to what we were looking for... No singing right away, which helped the viewer listen to the main character's voice much more.
http://www.danosongs.com/music/danosongs.com-thetimeisntright.mp3 - This we felt was also very good, but it had talking at the beginning (We also tried this track, turning the volume down and up, around the character talking.. but we felt it wasn't as effective.)