Audacity is the standard for free music editing software. It runs on everything, costs nothing, and can do just about anything you would need to do.
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If you live in Apple land you can use Garage Band for a slightly more friendly interface.
The big name in the music editing world is Pro Tools and they have a Free version called ProTools First that you could use.
Pro Tools - Music Editing Software - Comparison - Avid
Me Personally I used Studio One from Presonus because it's what my musician father uses.
Also FWIW the 99cents that I spend on each song for my show from Amazon, iTunes, or Google Music SO DRAMATICALLY improves the sound quality that IMO it's the way to go. I'm sure nobody will notice that 6 pack of sparklers you had to cut from the show to include music in your budget