Does that help?
I live in Podunk, and I haven’t had a non-holiday day off in weeks. I’ll have to drive to Albany (45 min) to find a real record store. For the moment, Walmart is the best I can do. I’m sorry.
Of course, next time I manage to wrench myself away from the ties of Crappy Retail Jobs and Cornfield Livin’, I’ll be searching a real record store (if FYE counts as such).
Stan Kenton. Some may argue that he’s a little late to be considered truly of the Big Band/Swing era, but he’s definitely one of the crowd.
Oh, and if you’re looking for a song where the band shouts, the gold standard is PEnnsylvania 6-5000, by Glenn Miller.
racinchikki, I think Gene Krupa’s what you’re looking for. Look for the recordings with Roy Eldridge and Anita O’Day (um, but you probably won’t find them in Wal-Mart.) You’d probably also like Louis Jordan, and Cab Calloway.
I think you’d probably also love the song “Big Noise from Winetka,” performed by Bob Crosby.
One that hasn’t been mentioned yet,and why I failed to mention him in my Krupa and Artie Shaw post is ** Lionel Hampton ** THE master of the vibes.Played with the masters,then formed his own band and later a combo.Get a listen to Flyin’Home-his chart topper.Had the album many moons ago.
On public radio is Bob Parlocha (DJ).Syndicated, he plays a 12 hr.set locally from 9 PM til 6AM.He operates somewhere out of the bay area,IIRC.See if you have a local station in your area and get the times.The only thing I have on my car radio at night.And right now as I’m typing this.Just heard Love for Sale with Miles,Coltrane and Bill Evans.He also goes back farther,and plays newer stuff,too.Some may suit.
He plays a good mix,plus he gives you the sidemen and leader of the records (you know those really big,plastic CDs) 
he plays after every couple songs.If you’ve heard something you really liked you could investigate further.There are so many names,so many styles,it’s hard to recommend just 1 or 2
For really swinging stuff I’d recommend:
Benny Goodman
Count Basie
Woody Herman
Artie Shaw
Duke Ellington
Glen Miller
The Dorsey Brothers
Lionel Hampton
Lots of the other artists (Fitzgerald, Holliday, etc.) were jazz vocalists first and foremost, and, while they certainly did swing, it sounds like you’re looking for more band arrangements and less vocals.
I’m betting you’d like Buddy Blue. Talkin Woman is a tune you just can’t help but move to. Check it out. You’ll be glad you did.
If you haven’t heard Louis Prima’s Jump, Jive and Wail then you’re missing out also. It makes ya do just what the title says.
By the way racinchikki, you can listen to some of Louis Prima’s music here: http://www.jimmyvincent.com/cgi-local/ultimatebb.cgi?ubb=get_topic&f=14&t=000051