James/Jimmy Rushing is amazing with the Count Basie Orchestra, as is Joe Williams.
The Village Vanguard big band was and still is amazing.
Edit: just realized the VVBB doesn't have any records. Their predecessor is The Mel Lewis Jazz Orchestra and also the Thad Jones-Mel Lewis Jazz Orchestra which both have plenty of records.
A current band I like with a bluesy singer is The California Honeydrops.
For the 20s, You cannot go wrong with the Louis Armstrong's Hot Five and Hot Seven.
1930s you've got Cab Calloway, The Chick Webb Orchestra (later run by Ella Fitzgerald, and she was by all accounts a fantastic band leader), and countless others. Benny Goodman was the first white bandleader to integrate his band in the US. He added Lionel Hampton (a black vibraphonist), first to his small group and then to the full orchestra. Lionel Hampton later had his own big band.
Soloists to look at are Lester Young, Coleman Hawkins, Billy Holiday. A woman non-singer to check out is Mary Lou Williams. She's a badass composer, bandleader, and pianist.
For 40s, the Billy Eckstein Orchestra is a very important band in the bebop genre. Big names are Charlie Parker, Dizzy Gillespie, Kenny Clarke, Ray Brown.
For the 60s, definitely check out Charles Mingus big band, nonet, anything he's in.
My favorite jazz record label is Impulse! Records. It's a safe bet that any record they published from the 60s to the 90s is fantastic.