There are sooo many swing and big band artists out there in the used records bins. Like, the Dorsey Brothers, Andrews Sisters, Glenn Miller, Benny Goodman (the Live At Radio City is an awesome album-- Gene Krupa on drums), it just goes on and on. More modern big bands: Al Hirt, Herb Alpert, Buddy Rich, Doc Severinson(sp) and two of my favorite contemporary big bands: Akiyoshi/ Tabackin Band-- Husband wife team of Toshiko Akiyoshi and Lew Tabackin, together and in separate projects, including solo efforts. I think they might both still be alive. And the Kenny Clark/ Francy Boland Band. Two great albums of theirs are "Smile" and "More Smiles". Very popular in Europe, check discogs... Buddy Rich has an accessible catalog with his big band. One of my favorite female singers of the swing and jazz era is Anita O'day.
Once you start your search you will find a lot of MONO recordings. I have a dedicated mono turntable/cartridge setup in each of my systems, but not strictly needed, any good elliptical stereo cartridge, like Denon, should safely play your mono records, just not the other way around, don't use a mono stylus/cartridge for your modern stereo records.