[Beren]

For recording your voice you can use FlexiMusic Wave Editor, here you can also add background music to it. If you wish to compose your own music and add a recorded voice along with your music, you can use Composer. Make a try.

[Terry]

Another plug for Audacity.
You've got nothing to lose if you give it a try.
All you need to do is import the music on one track
then record your vocals on another. Simple. Free. Effective.