jazz or swing

40 years ago, I shared with a guy who was mad on Miles Davis, and I it did nothing for me at all. Just recently I thought that I would give it another try and got a cut price triple CD of Kinda Blue/Porgy & Bess/Sketches of Spain and I just can't stop playing them! - but you are asking about the 30's:

I agree on the Ken Burns series, it was a great series, and I imagine the CD's do as well. If you can get the videos/DVD's or it's repeated on TV, it's an excellent introduction to jazz.

If it's really swing you're after, it's mass taste and largely out of copyright. If you go for the mainstream of Goodman, Elllington, Herman, Miller etc., you'll find that you'll be overwhelmed by the variety of packages, good and bad, at silly prices both in CD stores and TV/press advertised.