Help me build up a jazz album collection. Can you suggest a must have album?

Looks like all the old greatest albums of all time are covered.  

How about some newer greatest albums of all time.

Al Jarreau

Bob James

David Sanborn

Gregory Porter

Fourplay

Four80East

Norman Brown

Norah Jones

Lalah Hathaway

Sean Jones

any of these artist albums are fantastic.  

Going back to the old stuff. I'm shocked no one said:

Lee Morgan-maybe the greatest trumpet player of all time, and that includes Miles!

Oscar Peterson

Gene Ammons

Oliver Nelson

Blue Mitchell

Carmell Jones

Art Pepper

Many contributors said Art Pepper

Ken McCullough of stereophile can help you there. He has lots of videos on the youtube.

To understand jazz you need to go back to 19th century black American culture and the use of "code" words and expressions to obfuscate their meaning to anyone but those that "get" it. Ragtime music and piano rolls opened up new musical awareness and possibilities, and novelty acts and "jass" bands started to appear, often for the amusement of white Americans. Hip young college students were quick to embrace the music; the music had a status of "either you get it or you don’t". The cool kids got it.

New Orleans was already a musical center, and its multi-cultural cross-currents provided a fertile environment for jazz to fluorish. New Orleans was also a cultural touch spot where it was acceptable for white Americans observe and mingle in black culture (gambling, prostitution, and music being some of the big draws).

I would recommend Louis Armstrong and his Hot Five and Hot Seven recordings as a good intro to jazz. Go back and become familiar with ragtime, then just go up the river to Chicago., Soon, regional flavors of jazz were sprouting in metro centers all over the country.

Take it from there!
 

"Katanga" Curtis Amy/Dupree Bolton.