Well, regarding old STP, they didn't really change up the setlist between shows. Mostly they'd stick to the same setlist for a leg of a tour, and then change it the next leg.
Now, I think the current formation has a much greater chance at spontaneity. The DeLeo Bros and Kretz are pretty much able to play any song they've written without rehearsing, and Chester seems to have an encyclopedic knowledge of STP and an ability to pick songs up VERY quickly. So if they want to throw in songs they haven't rehearsed yet, I think they'd be able to pull it off just by doing a quick run-through during a soundcheck.
As far as deep cuts I want to see Chester sing... Just about anything, really. The man has shown he has the range to sing any STP song there is. I'd like to see him take a crack at Seven Caged Tigers (because it's my favorite STP song) and Wonderful, obviously. I'd like to see the band finally play Glide after all these years, and Chester can certainly sing it. I'd also like to hear him sing every song off of Purple, if possible.
I DON'T want to see him sing Plush, Wet My Bed, Art School Girl, Adhesive, Hello It's Late or A Song For Sleeping. Other than that, I think everything should be fair game.