that's a nice question, and I like that you've only left us 3 options for each.

Given the names you've named, I would have to say:

Jazz:
Thelonious Monk
(try Brilliant Corners, or either of the Genius of Modern Music comps)
Duke Ellington (any compilation, but Such Sweet Thunder will do for a work of unparalleled impressionistic genius, if a little untypical of Ellington in some ways)
Charles Mingus (the Town Hall concert) Because it summarises so much of early 60s soul/R&B in a beautifully sophisticated and at the same time savage way)

Blues
Robert Johnson (The Complete Recordings - you can get this on Amazon for next to nothing so this should be yr essential purchase whatever anyone says. But as it happens, he's pretty much IT as far as blues guitar stylists go
Mississippi John Hurt - others have already recommended stuff by him . They're right!
Narrowing it down to a 3rd choice is impossible. I mean, you should hear some Blind Lemon Jefferson, some Scrapper Blackwell, some Mance Lipscomb, some Lightnin Hopkins, all sorts of things. But speaking entirely personally, get some Pink Anderson. That's who I got into, purely arbtrarily, after Johnson and others, and he's a useful guitarist to listen to.

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Thanks.
-Joe Offer-

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