As the only chordal instrument, you and you alone can play chords under the soloist. However, full-blooded chords may work well in blues/rock and roll, but only sometimes in jazz. The occasional number will benefit from nice 5 or 6 string chords - maybe arpeggiated, but since the bassist will be rooting and fifthing to a degree, you can find the other notes - usually the 3rds, fifths (altered sometimes) and 7ths. Throw 9ths in as well if you can. So 2,3 or 4 note chords are good. Not strummed 4 or 8 in a bar, though. Comping is about leaving that space for the soloist, don't forget. The good news here is that those small chord are easier to learn than big ones!!
At solo guitar time, things will go a little sparse, as the chordal/rhythmic aspect will be missing. Keep it simple and just remind everyone how the original tune was supposed to go! With some subtle changes to the rhythmic and note elements. Maybe the sax will join in on parts of that.
A nice way to do something slightly different is to 'trade fours'. Choose a piece which splits easily, and play four bars, then sax plays the next four, then you again, etc.
At the gig, try to smile sometimes - if the audience sees that, it will A. join in. B. think you're having fun. C. feel that you're confident - even if it's not totally true...yet. But try to relax - we all play better in that state of mind and body.