Here are some names that haven’t been mentioned so far. As you can tell, I am biased toward early jazz:
Sidney Bechet specialized in soprano sax, although he also played clarinet. His playing could be beautiful and powerful at the same time. He had a long career and made many recordings, all during the 78 RPM era (he died in the 50s). There are Bechet collections - look for ones that include Summertime and Petit Fleur.
Bix Beiderbecke was a great cornetist who died young. He did some of his best work with Frank Trumbauer, a sax player who teamed with Bix on records like Singin’ the Blues and I’m Coming, Virginia. Bix didn’t sound like most of the other trumpeters and cornetists - he had a bell-like tone and a plaintive style without being very bluesy.
Joe Venuti and Eddie Lang were a violin/guitar duo who preceded (and influenced) Django Reinhart and Stephane Grapelli. Venuti played a great hot fiddle, while Lang was mostly an accompanist (although he did lead at times). Lang played a lot of single-string, which is something you don’t hear much from today’s jazz guitarists.
McKinney’s Cotton Pickers was a band from the late twenties and early thirties that played hot dance music. The most important member of the band was Don Redman, who did most of the arrangements (he was a pioneer arranger for Fletcher Henderson before he went to the Cotton Pickers). Some of their best pieces include Zonky, Plain Dirt, Never Swat a Fly and Ain’t I Good to You.
Bennie Moten led the greatest of the territory bands in the twenties and early thirties. A territory band was one that played outside of the major music centers of New York and Chicago. Moten’s band played out of Kansas City and created a distinctive sound (I can usually tell a Moten record within the first bars). The band went through a transformation when it hired a bunch of musicians from Walter Page’s Blue Devils. One of them was the pianist William “Count” Basie who, when Moten died in 1935, formed his own band and took many musicians from the Moten band with him.
Luis Russell was a Panamanian-born pianist who won the lottery and used the money to move to the U.S. He took over a band that had been led by King Oliver and transformed the sound by introducing swing - in 1929, several years before the swing era. Russell continued to produce fresh, exciting music until Louis Armstrong took over the band in 1934. Unfortunately, this was the point where Armstrong changed from a jazz innovator to a pop star. The band was never the same after that. There’s a very good CD collection on the Retrieval label called The Luis Russell Story - this collection has every side that Russell’s band recorded from the time Oliver left until Armstrong arrived.
The Mills Blue Rhythm Band is an often-overlooked favorite of mine. It was named for Irving Mills, a music publisher who also managed several bands, including Ellington’s for many years. Mills wasn’t a musician (he sang on a couple of records, but that’s it), and the membership of the Blue Rhythm Band changed a lot over the years. Still, they made a lot of great records. It was a swing band. I am ambivalent about swing - it could be great at its best, but it could also be dull, consisting of musical cliches strung together. The Mills Blue Rhythm Band was among the best at swing, in my opinion, in that their records often had imaginative arrangements and great solos.