Jazz Recommendations

I am just starting to get into Jazz. I recently bought Thelonious Monk Quartet "Live at Monterey" and was blown away. Could you recommend other mainstream Jazz recordings that I should have in a basic collection to help me get started.
Jazz: From It's Origins to the Present by Lewis Porter and Michael Ullman is an excellent introduction to jazz. It's a paperback text book. Very clear and easy to read. It explains why certain people or music are "important" and puts them into their historical context. You get a good sense of what the good artists and pieces are.

The book accompanies/tracks a jazz collection put out by the Smithsonian, as they sometimes go into specific pieces on that set. Try to pick one up cheap on half.com.

I use the Penguin Guide to Jazz and www.allmusic.com to learn more about artists and pick albums. They're choices are pretty straight ahead and obvious to the more seasoned jazz fan, but you won't be lead astray with any critic's unusual tastes.
It's a difficult matter to recommend favorite recordings. Besides what has already been mentioned, I can suggest two sources for further exploration. And exploration is the best way to find out what one likes as well as to understand why fans/critics appreciate particular artists/albums. They are: the Penguin Jazz CD guide and Downbeat magazine. The year end issue of Downbeat has a listing of the years best cd's. All I can say is keep on listening, take chances on that next purchase, go to jazz clubs and keep an open mind!
A nice approachable recent release that I found easy to warm up to, is Terence Blanchard's "Let's Get Lost". It features a variety of popular female vocalist singing Jimmy McHugh standards. Blanchard's playing is nice and tight and it's sonically well produced and recorded. Have fun.
to Professor Campbell et al, what an impressive thread! Having just stumbled upon it (my first real day off since the holidays), I've read each and every one of these posts, and must offer my own stamp of approval to nearly every recommendation that's been made here. I would add my own comments for Kaldec, only in that these were possibly overlooked by the many jazz enthusiasts who've posted here. There was no mention of Kenny Garrett's album, PURSUANCE: THE MUSIC OF JOHN COLTRANE, which is, perhaps, one of the finest releases by a new artist to appear in the past several years. As for noteworthy books, I'm sure that most of you would agree that Barry Kernfeld has contributed more than his fair share of good information on the music and musicians that make up this wonderful genre. Although his GROVE ENCYCLOPEDIA OF JAZZ is probably indispensible to the ardent fan, I think his BLACKWELL GUIDE TO RECORDED JAZZ is equally important. I'm sorry that I can't recommend a single album that is my all-time favorite; there are just too many of them that I couldn't possibly live without, but if pressed, I might have to say that THELONIOUS MONK WITH JOHN COLTRANE ranks among my absolute favorites. Happy listening!
Thank you all for your great insights. I have a large collection of recorded jazz, both on CD and vinyl.

Among my favorites available from Red Trumpet in better quality CD releases are:

Alto Sax
Art Pepper, Gettin Together (earlier period)

Big Band (avante garde)
Mingus, Mingus, Mingus, Mingus (if you like Au Um, listen to this)

Art Blakey, A Night at Birdland (with Clifford Brown) (timeless bop)

Bill Evans, Portrait in Jazz (great sound, one of his best)
Herbie Nichols, Blue Note recordings (see Spellman, Four Lives)

Tenor Sax
Johnny Griffin, A Blowing Session (wtih Coltrane and Hank Mobley) (terrific)
Sonny Rollins, Saxophone Colossus; Way out West (classic bop)

Armstrong and Ellington, Complete Sessions (also issued as Great Reunion) (if you have never heard this, you will be blown away)
Ella Fitzgerald, Ella in Berlin (includes famous rendition of Mack the Knife)
Sarah Vaughan, In the Land of Hi Fi (beautiful voice, great record)

Other terrific recordings that are among my favorites, which you may wish to consider, include

Alto sax:
Sidney Bichet, The Fabulous (New Orleans style)
Art Pepper, Straight Life (later period, incredible)
Sonny Stitt, Plays Bird (hard blowing bop)

Big Band
Count Basie, At Birdland
Charles Mingus, Au Um; Pethecanthropus Erectus
Oliver Nelson, Blues and the Abstract Truth (a classic)
Ella and Basie, On the Sunny Side of the Street (one of Ellas best)
Ellingotn, At Newport

Ellington, This One’s for Blanton (also the original Ellington/Blanton duets)
Bill Evans, Sunday at the Villiage Vanguard; Waltz for Debby
Jay McShann, Tribute to Fats Waller
Theloneous Monk, Solo Monk; At the Five Spot
Herb Nichols (see above-if you like Monk, listen to this)
Bud Powell, The Essen Jazz Festival Concert (inspired)
Horace Silver, Blowin the Blues Away
Ralph Sutton, At the Café des Copains (incredible stride piano)

Tenor Sax
John Coltrane, Coltrane and Hartman; Bags and Trane; with Ellington; A Love Supreme; My Favorite Things (soprano sax); Giant Steps
Stan Getz, Happy 50th
Dexter Gordon, Lullaby for a Monster; A Swingin Affair, Go, Stable Mable
Charlie Parker, Savoy Sessions

Louis Armstrong, Hot Fives and Hot Sevens (New Orleans style, important timeless music)
Clifford Brown, At Basin Street; Clifford Brown and Max Roach; and Best of Clifford Brown and Max Roach in Concert (I love Clifford Brown)
Miles Davis, Kind of Blue; Someday My Prince Will Come; Box Set
Lee Morgan, Sidewinder

Armstrong and Ellington (see above)
Bob Dorough, Yardbird Suite (sings Charlie Parker music, very interesting)
Ella Fitzgerald (see above: Ella and Basie; Ella in Berlin-two of her best)
Johnny Hartman, (see above: Coltrane and Hartman-a classic); Once in Every Life
Billie Holliday, All or Nothing at All
Helen Humes, 1947 (incredible); Songs I Like to Sing
Alberta Hunter, Amtrack Blues
Eddie Jefferson, The Jazz Singer
Helen Merrill with Clifford Brown (wonderful music)
Carmen McRae, Carmen Sings Monk; Lover Man and other Billie Holliday Classics
Anita O’Day, Anita Sings the Most; Pick Yourself Up
Maxine Sullivan, With Her Swedish All Stars Vols 1-3 (hard to find, but great)
Sarah Vaughn, with Clifford Brown (also, see above-In the Land of Hi Fi) (essential music)
Dinah Washington, Dinah Jams (contains one of the greatest trumpet solos); The Swigin’ Miss “D”

Believe it or not, I actually tried to keep this list as short as possible. It is not intended to be anything but a personal list of some of my favorite recordings.