If you haven't listened to much jazz, maybe try picking up the Smithsonian collection of Classic Jazz. Start at the beginning. 5CDs of some of the most important tracks in the history of jazz. Of course any collection will miss out on some tracks. But this was is a good place to start. This collection is strong from Louis Armstrong to 1960. It doesn't really have much after that.
Amazon.com: The Smithsonian Collection Of Classic Jazz: Various Artists: Music
Some of my favorite trumpet tracks included:
Struttin' With Some Barbecue - Louis Armstrong
Hotter Than That - Louis Armstrong & His Hot Five, Louis Armstrong
West End Blues - Louis Armstrong & His Hot Five, Louis Armstrong
Weather Bird - Louis Armstrong, Earl Hines
Concerto for Cootie - Duke Ellington's Famous Orchestra - Cootie Williams
I Can't Get Started - Dizzy Gillespie Sextet
Shaw 'Nuff - Dizzy Gillespie All Star Quintet, Dizzy Gillespie
Boplicity - Miles Davis & His Orchestra
Summertime - Miles Davis, Gil Evans Orchestra
Pent-Up House - Sonny Rollins - Clifford Brown
So What - Miles Davis Sextet
Lonely Woman - Ornette Coleman Quartet-Don Cherry
Also you can get the Smithsonian Collection of Big Band Jazz: the beginning to the 50's
These will get you started.