So based off of previous performances by the band, interviews they've given concerning the upcoming shows, and this rehearsal I think it's safe to say the following songs will more than likely be included in the upcoming setlists:
"Dead and Bloated", "Sex Type Thing", "Interstate Love Song", "Wicked Garden", "Vasoline", "Trippin On A Hole In A Paper Heart", "Sex & Violence", "Pop's Love Suicide", "Piece of Pie", "Out of Time", "Church on Tuesday", "Big Bang Baby", and "Sin"
Then, as Robert told Brett, they may be playing "Take A Load Off" and "Fast As I Can".
Of course the setlists will probably switch up a little, and different songs will be played but the above seem likely to be performed at some point during the tour.
As for how many songs, I'm not sure how similar Chester is planning to make these shows to LP shows, but traditionally at a Linkin Park show they will play about 22 songs (full set and 3-4 song encore) and the show will last at least 90 minutes. However; Linkin Park's songs though are typically short, whereas quite a few STP songs push or exceed 6 minutes. That may impact the amount of songs that will be played.
Either way, I imagine they'll play at least 1-2 new songs so going off of the above and the new songs I think it's safe to say the show will be a really solid mix of deep cuts, greatest hits and new material.
*Fingers crossed for Crackerman*