Go to jamstudio.com This is a free limited access site where the students can create original music for use in projects. It's easy and fun. There are educator grants available for full access if you wish.
Musopen has public domain classical music recordings.
Besides public domain, you could also use Creative Commons music and just make sure your students give credit to the musicians in their work. Here's several sources for Creative Commons music: Purple Planet Magnatune Creative Commons: Search OWL music search or SpinXPress
Yes, the sheet music or score itself would be public domain, but particular performances may be copyrighted and require a license for use. You're deal with two different aspects of copyright here.
Musopen explains it this way:
"The copyrights that apply to music are complicated. Put simply, there are at least two copyrights to any sound recording of a musical work – the copyright on the underlying composition and the copyright on the particular performance. So, for example, if you perform the song “Imagine” by John Lennon, John Lennon’s estate holds a copyright in the sheet music, and you hold a copyright in your performance, but you are limited in doing certain things with the recording of your performance without John Lennon’s estate’s permission or a statutory license."
It's not straightforward. If you find recordings from the US Marine Band or US Air Force Band, those recordings are in the public domain (produced by the government & paid for by taxes = public domain). So, if the music itself is old enough to be in public domain, then the recordings in those cases are safe too.
Generally, though, it's really hard to find truly public domain recordings where both the music and the specific performance are public domain. A collection of historical recordings would probably do it.
Honestly, music copyright is complicated enough that I generally think it's safer and simpler to just go with Creative Commons and cite the source. At least then you know what you're using is OK because the artist has labeled it clearly.
Who knows, better to be safe than sorry---I got a big handslap for using We Are The World in a presentation in front of the school board several years ago--- I've taught workshops on copyright and thought I was within the guidelines of fair use---it was then pointed out to me that the BOE was a public forum (which of course I knew)!!! Yikes.