Jazz Recommendations.

The two CD set from Columbia/Legacy: "The Essential Dave Burbeck"

Personally, I wouldn't start off with the standeard recommendations like Miles Davis, Coltrane, etc. I would recommend some of the more assessible jazz from the 50's & 60s, by such artists as Bill Evans (piano) Oscar Peterson (piano), Stan Getz (sax), Ray Brown (bass v) Art Pepper (sax), Monty Alexander (piano), Ben Webster (sax), Jerry Mulligan (b. sax), Dave Brubeck (piano), and for some what latter (date wise, not style wise) Andrew Previn (piano), Houston Person (sax) and for jazz with a little flavor of swing, Scott Hamilton. Mostly they have their own trios or quartets, doing standards.

Assuming that you are meaning jazz in the more traditional vein--as opposed to 'smooth' jazz--this is a fun place to start, although some of the albums will require a more lenient ear if you're not so accustomed to jazz.
http://www.scaruffi.com/jazz/best100.html

A couple others that get my vote:
Tomasz Stanko - Suspended Night
Wayne Horvitz - Sweeter than the Day
Achim Kaufmann - Double Exposure

Enjoy!
Howard

What type of Jazz? It's a pretty diverse art form that spans almost a century. Big Band? Ragtime? Bebop? Hardbop? Free Jazz? Fusion? Etc.?

That aside, I'd add for anyone listening to jazz: Coletrane "Giant Steps".

More later.

I would recommend the following albums because they have enough melody and a blues feeling that a non-jazz person can relate to, but are still first rate classics: The Sidewinder by Lee Morgan. Midnight Blue by Kenny Burrell. Ballads by John Coltrane. Coop by Bob Cooper. They are all still in print and easy to obtain.