I fool with some residential & commercial building glass at work & just a little automotive occasionally.
Most of the professional automotive glass shops mainly use fast dry urethane in large sausage type tubes. This stuff is so stiff an electric sausage caulk gun is pretty much mandatory. No worries because the strength of any average good standard dry time urethane in a 10 oz tube is sufficient. Just give it a few hours to set before driving.
There are some primers for both your painted window channels & glass, but you shouldn't need any. Cleaning surfaces with isopropyl alcohol should be plenty sufficient.
I'm not an expert on auto window gasketing trim, but I'm pretty sure you just do a proper caulk bead to the installation area, thick enough, but not overly messy, set glass in place & your done with the trim. Urethane can & does hold certain rubber trims in place, but in your case it's made to be in place for you to be done with quicker & not mess with a separate installation item.
A 2nd set of careful hands can take the place of glass cups, reaching around from inside.
Auto parts stores, such as Advance auto sell 3-m windshield urethane , but at over 20 bucks a tube, that's ridiculous. I talked in person to a glass shop & bought a couple of 10 oz tubes for approx. 7 bucks each recently. Watch the expiration dates on this stuff carefully, approx. 1 year from mfg shelf life.
In my area, there are mobile people working for themselves that can be cheaper than going to a shop. I've bought caulk from one around 5 bucks a tube & seen entire windshield installs inc glass done for around $100 to $120 in some cases. Safelite glass owns the local supply warehouse people buy from.