What a wonderful thread! I could write on this for days.
The cool thing about these genres (and any musical genre really) is that for every person you list there are literally ten other people that are just as much fun to listen to. And everything is related. You can start with Count Basie -whose guitarist Freddie Green was a seminal influence on Chuck Berry- and with just a hop skip and jump wind up with Richard Thompson- who is by no means a blues player per se but skillfully employs Chuck Berry licks in his live version of "Hokey Pokey". Ultimately everything's related.
That said there are just so many different types of blues and jazz that it's hard to know where to start.
Just from the top of my head and the numbering is NOT anything to do with quality or importance
1)
T-Bone Walker -A very skilled guitarist in both jazz and blues genres and someone who influenced EVERYONE who came after him, including people like Chuck Berry, BB King, Albert King, etc. Anything he did in 40's and 50's is gold. He's the songwriter of the classic "Stormy Monday". Both he and Pee Wee Crayton define the word elegance. He played a very smooth uptown jazz-blues hybrid music that just dripped confidence and class. No down home shouting for him.
2)
Charlie Christian-A contemporary of T-Bone who leaned more towards jazz than blues but gave Benny Goodman's group an infusion of talent and swing.
3)
Pee Wee Crayton-Another contemporary of T-Bone Walker's. I think he was a little younger. He also straddled the line between blues and jazz. Again, his work from the late forties and fifties is sublime. GREAT singer and guitarist.
4)
Ike Turner-Originally a pianist, he released what's been called the first "rock and roll" song-Rocket 88. Turner had a much harder guitar sound and was one of the first ones to deliberately use distortion and pinch harmonics. His later work with Tina made him more money but generally speaking his pre-Tina work is more inventive.
5)
Roy Buchanan-Speaking of harmonics, Buchanan was able to produce them on demand. He was from the Ozarks and had a more country influenced sound. He was often called the best guitarist no one's ever heard of. Check out anything he did in the early seventies. Although he did not play steel guitar he could effortlessly sound as if he did. He wasn't a great singer though. Like Hendrix he "sang" through his guitar.
6)
John Coltrane-Imagine if God played saxophone. I can't say anything more than that. You may want to avoid initially his post 65' stuff as he was more into "free jazz" at that point which is not everyone's cup of tea.
7)
Rahsaan Roland Kirk-A blind jazz multi-instrumentalist who practiced circular breathing and played several ancient saxophones, Kirk's work is solid quality no matter which period you choose from. One talent of his was playing different melodies on multiple reed instruments simultaneously.
8)
Etta Baker-A blues guitarist from North Carolina, Baker was primarily acoustic fingerstyle-a style which was different than everyone above and post WW2 was primarily associated with folk, not blues. Good stuff.
9)
Albert Collins-A blues guitarist from Texas who played a shuffle style which has come to be replicated in bar bands across the world. He played the guitar like an organ. His music was fun but not super complex.
10)
John Lee Hooker. He was a direct link back to Africa. Much of his music-especially his solo stuff was full of drones, odd time signatures and space. It sounded eerily close to music from Mali and Mauritania. You have to be very careful getting anything by him though as he recorded for close to 60 years with a variety of bands and conditions. Because his timing was defiantly irregular it was often difficult for less skilled bands to follow him.
11)
Sonny Sharrock, A guitarist who famously claimed not to be a guitarist. He saw himself as a saxophone player. He translated Coltrane's "sheets of sound" method to the guitar. Again this could often result in cacophony so his music is a very acquired taste but as a Hendrix contemporary he used tones and styles that were just as much associated with hard rock as with jazz. His early seventies work is worthwhile.
12)
Howling Wolf. A giant of a man with a giant of a voice. See if you can get the Chess Box set. A lot of his music anticipated and was influenced by funk. When you listen to his sixties work you can hear the family relationship with James Brown's bands at the time.
13)
Muddy Waters-Can't mention the Wolf without mentioning his label mate and rival/friend Muddy Waters. Both as a guitarist and singer Muddy defined the Chicago Blues sound-which was very very different than people like BB or Albert King. Again, there is a Chess Box set. I think Wolf had funkier bands though. Muddy rarely employed a horn section. Everyone got to solo but usually the primary soloist was whoever was the harmonica player; he had some great ones. However to me, unless you REALLY are that good, a little harmonica can go a LONG way.
14)
Etta James-She is a singer who stands at the crossroads of blues, jazz, soul, rock and roll. Anything she did in the fifties or sixties is definitely worth picking up.
15)
Elmore James-The definitive slide guitarist. He built his own amps and had a heavy thick tone that anticipated the metal of the seventies. His singing voice could best be described as tortured. His mid fifties bands rivaled Muddy's and Wolf's as the best in blues.
And many more that I didn't mention...hopefully others will.
Again, great topic!!!
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I sometimes wonder if Dizzy Gillespie, Louis Prima, Clifford Brown, or Clark Terry ever went over to Miles' house and told him gently: