Gordon, do you have a good turntable?
If so, I would recommend scrounging places that sell used records to try and find Time-Life's The Swing Era. It was a series of records, a boxed set for each time period, along with a well written book in each. That series virtually ran the full history of Big Band & Swing from beginning to end, and in most cases recorded with the original bands, and very faithfully to the original recordings. Recording quality seems to vary somewhat from one record to another, but for the most part it was really well done. That record series started in the late 60s and lasted though the early 70s. I'd love to see that series reissued on CD.
On CD, there are some really good albums out there as well. In particular if you like Sing, Sing, Sing, the soundtrack to the movie Swing Kids has a recording of it that'll make you hair stand up! Good movie too.