Okay, I'm sufficiently bored to have another crack at this.
Early Jazz:
- Louis Armstrong (should go without saying): get a collection of the Hot Fives/Hot Sevens recordings. Columbia has done some amazing reissues of them - if you don't want to shell out for the whole lot, just buy volume 3. Also, Louis Armstrong Plays W.C. Handy is one of the essential jazz albums.
- Bix Beiderbecke: get the (old) Columbia compilation Singin' the Blues. That'll do you good.
- Sidney Bechet: Runnin' Wild is a great album. Get it.
Swing:
I've already done Big Band, so here's some small group stuff well worth getting:
- Lester Young: the "Kansas City" Sessions. If you can find a C.D. of this that just has the master takes, that's the one you should probably get. If you like somewhat mellow, but still hard swinging music this will be right down your alley. Also, try to find (under Count Basie's name) a compilation with the following four tracks on it: "Shoe Shine Boy", "Evenin'", "Boogie Woogie (I May Be Wrong)" and "Lady Be Good". Lester Young is incredible on these recordings. Other great albums featuring Young: Lester Young With The Oscar Peterson Trio, Pres and Teddy (featuring some gorgeous piano playing from Teddy Wilson).
- Ben Webster: most of his best stuff was done in the '50s. Get Ben Webster Meets Oscar Peterson, it's one of the best jazz albums ever. Also consider Coleman Hawkins Encounters Ben Webster. Which brings me to . . .
- Coleman Hawkins: the first great tenor saxophone player in jazz. There are masses of compilations called Body and Soul - the one put out by R.C.A. Victor is great, and features the title tune which is one of the greatest single recordings in jazz history. Also worth getting is the Hawk Flies High.
- Benny Goodman: if you can find a good-priced compilation of his trio/quartet recordings with Teddy Wilson, Gene Krupa, and Lionel Hampton, buy it.
- Ella Fitzgerald: both the Cole Porter Songbook and the huge George and Ira Gershwin Songbook are well worth your time and money. For something a little less formal, try the Duke Ellington Songbook.
- Billie Holiday: get any decent-sized compilation of her early (1930s-1940s) Columbia recordings you can get. Columbia itself did an absolutely stunning job of remastering these a few years ago. These are some of the greatest and most enjoyable recordings in jazz history.
Be-Bop:
- Charlie Parker: should go without saying. Get a compilation of the Dial master takes. Should be pretty easy to find a cheap version. Parker's quintet at this time featured a very young Miles Davis. Also, a couple of live recordings well worth picking up: the Quintet: Jazz at Massey Hall and Town Hall, New York City, June 22 1945, both with Dizzy Gillespie. Speaking of whom . . .
- Dizzy Gillespie: get a compilation of the R.C.A. Victor big band recordings. These are incredible, especially "Manteca"
- Charles Mingus: I'm putting him here to make things easier, because Mingus is pretty much uncategorisable. If you buy no other jazz album, then buy Mingus Ah Um. It's that good. Also brilliant is Let My Children Hear Music. There are so many good albums by Mingus that it's almost impossible to write a shortlist - try also Blues & Roots, Mingus At Antibes, the Clown, Pithecantrhopus Erectus, and the aforementioned the Black Saint and the Sinner Lady.
- Sarah Vaughan: her self-titled album (also sometimes known as Sarah Vaughan With Clifford Brown is terrific.
- Betty Carter: try to find [the Audience With Betty Carter[/i].
- Thelonius Monk: get a live recording by his famous quartet featuring Charlie Rouse. Live at the It Club - Complete is a good one. Also, as far as studio albums go, buy Monk's Music.
Cool:
One of the more stupid labels in jazz, but we'll let that slide for now.
- Gerry Mulligan: get a compilation of the original recordings with the Quartet, featuring Chet Baker. Also well worth getting is the C.D. of Lee Konitz playing with this group.
- Stan Getz: the Steamer, West Coast Jazz and Stan Getz-Bob Brookmeyer Recorded Fall 1961 are all great albums.
- Miles Davis: like Mingus, uncategorisable. But a lot of people like to put him under "cool jazz" so who am I to argue? My personal favourite jazz album of all time is the (original) Miles Davis Quintet's 'Round About Midnight. This particular group put out a whole string of great albums in the 1950s - Relaxin' and Cookin' are the other two best in my opinion. Also, check out Birth of the Cool.
Hard Bop:
- Clifford Brown/Max Roach: the Clifford Brown-Max Roach Quintet was one of the great bands in jazz. Get their self-titled album. A Study in Brown, despite the title, is also worth getting.
- Art Blakey: Art Blakey's Jazz Messengers With Thelonius Monk is a great album.
- Lee Morgan: the Sidewinder.
- Kenny Dorham: Una Mas. Also, the Complete 'Round About Midnight at the Cafe Bohemia.
. . . And that's about where I get off. Have fun! If I think of any more I consider essential I'll post 'em.