you likely already have 'Jazz Party In Stereo', Duke Ellington. if not; it's a great place to start.
anything by Harry James; the Sheffield Recordings are all sonic wonders....'King James Version', 'Comin From A Good Place', and 'Still Harry After All These Years'....are all one's to find. the Lps are direct-to-disc and must haves.
Sinatra and Basie, 'It Might As Well Be Spring' really rocks as big band. I have the original Capital pressing as well as the CD which is great. I actually have 2 copies of the Cd which I used for years to compare redbook players side by side. 'Fly Me To The Moon' is an epic cut.
Louis Armstrong-Duke Ellington recording that is wonderful. The Great Summit. Great double CD, or Lp, the 45rpm is amazing. 'Duke's Place' is one of those tracks that soars and soars.
You can't go wrong with Woody Herman. A lot of the late Concord releases are quite good and are easy to pick up on the cheap via EBay. Just picked up "Woody's Gold Star" which is quite nice. Some of the 1950's-1960's recordings on Phillips are excellent like "Swing Low Sweet Clarinet".
Gordon Goodwin has several outstanding CDs with a modern take on big band.
I like the Mosaic reissue of Ella and Ellngton at Cote D'Azur.
Gene Harris and the Phillip Morris Superband is also worth seeking out.
The JATP recordings are of variable quality, but several are quite good.
The SF Jazz Collective has a shifting roster....my favorite is the CD of Monk tunes.
Look for Phil Kelly and the Santa Ana Winds who are one of the best big bands.
Basie's "Farmer's Market BBQ" is well recorded and classic Basie. Find "Kansas City Suite" on Roulette.
Clifford Jordan Big Band "Live at Condon's" and "Play What You Feel"
David Murray Big Band "Live at the Sweet Basil" is killer music
If you want to hear a high quality new (2010) recording of a band that plays Gershwin big band more similarly to old-school recordings from the '40s, try this one. Its a lot more quaint, but it has a charming swing to it. There is one original 'scratchy' recording...and the rest is all new.
Big Band is my favourite genre of music, and I often demo with it - and my favourite album of my favourite genre is:
Count Basie's Me and You - side one is big band, side two a smaller group.
Other albums besides some already mentioned above:
Al Grey and the Basie Wing - Last of the Big Plungers
Edmund Ros and his Orchestra - Ros on Broadway
Les Brown and his Band of Renown - Goes Direct to Disc
Warren Covington and his Commanders - Shall We Dance?