For a first transcription, I'd suggest a slow blues. Try Lester Young's "Back To The Land":
YouTube - Back To The Land - Lester Young. Or, Wes Montgomery's "The Thumb" (you don't necessarily need to do the octaves like Wes does, just single-notes).
Almost any Miles Davis solo is good (like Derek said). He doesn't play all that fast, most of the time. And his phrasing is excellent. Stay away from most other trumpet players at the beginning, though (like Woody Shaw or Clifford Brown) - they like to do super fast chromatic runs and it's really hard to hear unless you use a "slower downer".
You might want to look into Hank Mobley. Great saxophonist and very melodic - you won't have to spend a lot of time figuring out wacky extensions/alterations. JJ Johnson is also a good one to check out. He's a great bop trombonist.