Copyright in music is especially tricky. The score and lyrics, and the "expression," are copyrighted separately. Even if the copyright held by the composer has fallen into the public domain, there may still be copyright held by the musicians who performed it in the recording you have. Just because a song predates 1922 doesn't mean that a recording of it is in the public domain. If, for example, Coldplay made a 2009 recording of "My Darling Clementine" (unlikely as it may be!) an MP3 of Coldplay's "My Darling Clementine" would be protected by copyright. The score and lyrics would not.
Creative Commons musical works are not in the public domain. They are published with a license that specifies what you can do with them. You are allowed to use them without permission and without any charge, but you must follow other specified restrictions, which are explained here:: http://creativecommons.org/licenses/
Be careful of using any work with ShareAlike license, because often we cannot abide by its requirements. Faculty contracts and SUNY rules stipulate that faculty retain copyright to the courses they create, and that would violate the ShareAlike license. It's ok for things made by students and professional staff as long as you put a CC ShareAlike license on it.
Music from iTunes must be purchased by each user; however it is affordable enough that asking your students to purchase a playlist may be reasonable. While you cannot embed content in a webpage or Angel course, you can create a playlist and link to it. Music is downloaded from the iTunes Store (available through the iTunes Player) and may be played on a computer as well as an iPod or iPhone.