For me, the starting point is that I like the music. Given that, and maybe an openness and interest for experiment you're ready to go. Jazz is a wide field with lots of variation, so you can find percussionists with lots of equipment and action:
Other variants include ethnic jazz, jazz-rock, cross-overs into reggae/hiphop.
Some musicians move quite a lot (see Stan in the first image of this thread), though that brings difficulties in poor lighting.
Often performers come forward to front of stage for their solos.
There is some unspoken communication between band members, which I find interesting, like the look in Matt PineBomb's photo a couple of posts above.
You can get the more introvert moments, like your own shots above; portrait photography of a kind.
Small venues, where you're close to the performers.
Groups vary from small to Big Band.
Little or no hassle getting permission.
Above all, enjoy & don't get in the way of the other people in the audience.
[Edit 06/2017: restored image formerly hosted by photobucket]