You've got a lot of great recommendations so I won't give you another list, but when you're shopping don't overlook the Concord Jazz label. The are usually excellent LP's and they have a lot of very high quality musicians often not appearing elsewhere.  

Anything from Johnny Hodges  (Dukes first sax), Stanley Turrentine, George Benson-Giblet Gravy (early years), Count Basie, Lavay Smith and the Red hot skillet lickers (excellent vocals and masters of jazz instruments ensemble). Anything from Duke Ellington. Julian Cannon ball Adderley. Grover Washington Jr. (one of the smoothest sax's)  Kenny G! ...Im totally kidding :-)

Matt M

Hiatus Kaiyote  Choose Your Weapon

Is this a jazz album? To be jazz does it have to be on 60  to 70 year old structures?

I guess I'm asking what is jazz?

Dexter Gordon “One Flight Up”. 

Isao Suzuki Quartet ,Blow Up, Japanese Jazz