Here are a few that I recommend:
Duke Ellington - Never No Lament: The Blanton Webster Band
This 3 CD set cherry picks the best cuts from the mammoth 25 CD RCA Duke
Ellington centennial boxed set. You get 75 tracks featuring the talents of
Jimmy Blanton, Ben Webster, Johnny Hodges, Ray Nance, Cootie Williams, Rex Stewart,
Billy Strayhorn, et al. This was perhaps the best band Ellington ever led and was
arguably the greatest band of the swing era. This is beyond essential listening.
Cab Calloway - Are You Hep to the Jive?
The 22 tracks on this CD are taken from recordings from 1939 to 1947. Calloway
always had top flight talent in his band. Even Dizzy Gillespie did a short stint with
Calloway. At $6.99 on Amazon.com this CD is a steal.
Count Basie - The Complete Decca Recordings
I know you asked for recommendedations on 1940s music but I have to cheat
a little here. This set includes everything the Count Basie Orchestra recorded
for Decca between 1937 and 1939. This music features none other than Lester
Young on tenor sax, and for that reason alone it is too important to pass up.
Glenn Miller - The Golden Years: 1938-1942
During the 1930s and 40s (the swing era), jazz became the dominant
form of American popular music. So the lines between pop and jazz
were somewhat blurred. But Miller's recordings often lacked something
that was always a core tennent of jazz: improvisation. Still, whether
you call it jazz or pop is beside the point. It is great music. This inexpensive
4 CD set from Proper Box UK is outstanding. There are 98 tracks and just
about every single hit Miller recorded at the height of his popularity is
here.
--Jerome