For the love of all things holy, get Mingus, Ah Um by Charles Mingus. It's the best Jazz album I've ever heard. While far from a jazz buff, I've heard a fair amount, and Mingus Ah Um wins. Coltrane - Giant Steps and Miles Davis - Bitches Brew are kinda obligatory. Other than that, I'm a big fan of Ornette Coleman.
Basically though, you want Inlander on the case. That's who I went to for Jazz Recs, and I'm thankful I did.
Aww shucks, I'm glad you like the Mingus! For everyone else, here's the list I sent to MilkmanDan when he asked me for recommendations (there's a hell of a lot that's not on here, which I'll probably elaborate on later):
1920s:
- Louis Armstrong:
Hot Fives and Hot Sevens, volume 3 - Bix Beiderbecke:
Singing the Blues 1930s:
- Lester Young:
The 'Kansas City' Sessions - Count Basie: If you can find a C.D. of the 1938 Decca recordings, grab it. Failing that, anyu compilation of the '30s stuff would do the trick - but make sure it has "Jumping at the Woodside" on it!
- Duke Ellington: Try and find a compilation of the early '40s R.C.A.-Bluebird recordings - a few tunes to look for: "Ko-Ko", "Jack the Bear", "Concerto for Cootie". These are all amazing orchestral recordings.
- Billie Holiday: You should be able to track down a compilation of her '30s recordings. Focus on the Columbia releases - these are her best, and the sound quality on the recent reissues is unbelievable.
1940s:
- Charlie Parker: get a copy of the Dial master recordings. This is absolutely essential! If you stick to the masters rather than the complete Dials, you should be able to get it for in a fairly cheap 2-C.D. set, but you might be struggling to get a single C.D. If you somehow manage to find one, the East Coast Dial recordings are the ones to look out for.
Dizzy Gillespie: Try and find some of the R.C.A.-Bluebird big-band recordings - these are amazing. If you don't get anything else, at least get the tune "Manteca" (the original studio recording, that is.)
1950s:
- Miles Davis: a whole swag of recordings, but two that are particular favourites of mine are
Round About Midnight and
Miles Ahead - the former is small-group, the latter is orchestral arranged by Gil Evans.
Round About Midnight features a young John Coltrane on tenor saxophone.
- Charles Mingus:
Mingus Ah Um is one of the great jazz albums. It's probably also Mingus's most melodic album. For some of his more avant-garde stuff, try The Black Saint and the Sinner Lady from the '60s, or Let My Childeren Hear Music from the '70s.
- Gerry Mulligan: you should be able to get a single-disc selection of the recordings made by Mulligan's famous pianoless quartet with Chet Baker. Also check out a great big-band C.D. by Mulligan's Concert Jazz Band, called
At the Village Vanguard.
- Ornette Coleman:
Free Jazz. Just like the title says - if you're feeling adventurous!
- Sarah Vaughan: Self-titled. Brilliant jazz vocal album, with a great band in support.
1960s:
- Bill Evans:
Waltz For Debby. Pretty much as good as jazz gets.
- John Coltrane:
A Love Supreme - though you might already have this.
To be honest I don't really get into fusion and all that stuff, so I can't recommend you anything much from the '70s and '80s. A few other slightly less famous albums to look out for, though, are:
Nothing But the Blues by the guitarist Herb Ellis,
At the Cafe Bohemia or
Una Mas by Kenny Dorham,
Clifford Brown and Max Roach by, well, Clifford Brown and Max Roach . . .
I would also consider "Louis Armstrong Sings W.C. Handy" to be absolutely essential. Likewise "Ella Fitzgerald Sings the George & Ira Gershwin Songbook" - although that's a 4-C.D. set, which might be more than some people are willing to commit to! Oh, and before I forget:
Ben Webster Meets Oscar Peterson. Also
Coleman Hawkins Encounters Ben Webster Screw it, this topic's too big for one post!!
EDIT: Oh, and as for Moiche's recommendation of the Massey Hall concert - there was a limited-edition print of it a few years ago, with some fancy jiggery-pokery done to the remastering, and the sound quality is a bajillion times better than on other versions. I think it was only limited to 10,000 copies or something, but if you can get your hands on it then do so.