Definitely an alto sax. Not kidding. If you had to equate genres with instruments the sax and jazz would be perfect. The sax and piano (rag-timem etc.) pretty much created jazz.
Pretty much brass/bass instruments go well with jazz, though. Woodwinds are kind of iffy, especially the flute. (I do understand the sax is a woodwind but come on, everyone knows it's a brass posing as a woodwind). Clarinets can get away with jazz, too. Strings are kind of iffy, too, as in classical strings. I've never heard of a jazz violin, but you never know. Contra bass would definitely be jazz on the other hand.
So. Alto-sax, trumpet, trombone, bass guitar, and clarinet in order of best to least best. (Excluding piano cause piano is the BOSS)