The above posts recommend Blues, here are some thoughts on JAZZ...
As a teenager I grew up with Rock, Hard rock, and Progessive Rock.. at age 16 or so I began to wade into the waters of Jazz... my first Jazz records were predictably Jazz-rock fusion, some of which are still my favorites today:
1. Return to Forever - Romantic Warrior
2. Weather Report - Heavy Weather, Black Market, Tale Spinnin
3. Stanley Clarke - School Days, Journey to Love
4. Jean-Luc Ponty - Imaginary Voyage, Enigmatic Oceans
5. Jeff Beck - Wired
And many other similiar titles... John Mclaughlin, Soft Machine, Al Dimeola, etc.
My first REAL Jazz albums purchased at age 17-18 were:
1. Chick Corea - Inner Space (still one of my favorites today)
2. Miles Davis - Water Babies (my first of twenty or so Miles Davis album purchases
3. Buddy Rich - Class of '78 direct-to-disk (I ran out and bought this at age 18 the next day after seeing Buddy Rich and his big band close up in a club in Rochester, NY... really changed my ideas about "who is a good drummer")
4. Oregon - Roots in the Sky (a challenge to my 18 year old sensibilies, became a favorite)
5. George Benson - Breez'in (his best, hands down IMHO)
At this time in college I met a young jazz musician who began teaching me some jazz theory and gave me the following jazz recommendations to get me started (and I'll give these to you)
1. John Coltrane - Blue Trane, A Love Supreme, Ballads, Lush Life
2. Miles Davis - Sketches of Spain, Kind of Blue, In a Silent Way, to start with
3. Dave Brubeck - Time out
4. Cannonball Adderly - Something Else
5. Lee Morgan - the Sidewinder
6. Herbie Handcock - Maiden Voyage
Other names(Jazz standards):
Sonny Rollins, Dexter Gordon, Art Blakey, Gerry Mulligan, Thelonious Monk, Stan Getz, Duke Ellington, Bill Evans, Charlie Byrd... and many others
Some "advanced concept" Jazz artists:
Keith Jarrett, Art Ensemble of Chicago, Ornette Coleman, Sun Ra, Cecil Taylor, George Russel, Don Cherry, others...
Or, try ANYTHING on the ECM jazz label.. an instant adventure. I recommend Ralph Towner, John Abercrombie, Terje Rypdal, Eberhard Weber, the earlier Pat Metheny pieces, Egberto Gismonte.
Anyway it's nice to see someone interested getting into jazz.