If you’re a straight up, traditional jazz player, then you’ll probably want an instrument that reflects that. Hollowbody guitars have been the choice of jazz players for decades, due to their tremendous low end response and warmth. You do sacrifice some sustain, which is worth bearing in mind, though that can work well for a lot of jazz music.
Hollowbody guitars can also be prone to feedback if you’re playing close to a really loud amp, or you’re using a fair amount of overdrive. For a lot of jazz styles, this shouldn’t be a problem, but if you know that you’ll be playing sections with gain, then a semi-hollow or solid body guitar should help with this.
If you’re likely to be fusing jazz with bits of rock, blues, country or anything else, then you might want something a little more versatile. You’ll still want that mellow warmth, but you might want a little more bite and brightness to your tone at times - guitars with a couple of different pickups on board can prove to be incredibly handy in these situations.