One can play jazz on any instrument, but some work better than others. (Please, no bagpipes, oboe, bassoon, french horn, or harp.) For me, 10-string blows away my violin or viola. Not only easier to amplify, it serves as a comping instrument, without piano or guitar.
An associated question is, do you want to stay in the trad-jazz/swing genre of old stuff? If you want to join with the icons of jazz, Parker, Coltrane, Monk, Sonny Rollins, Miles, Bill Evans, Jm Hall, etc., and newer names like John Scofield and Michael Brecker, go electric, with a C course. Best, convert a 5-string to 10 for the richer tone.
One genre that welcomes everybody blowing is contra dance. Instrumentation is ad hoc, often with winds like flute and saxophone. My contra band is piano, acoustic 10-string, violin, and flute. We vary the sound, sometimes unison, sometimes one solo, and sometimes a free-for-all. Tunes edge into rags and marches, but are mostly reels and jigs.
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