I tow my PUP with my Avalanche (1500) which is the same platform as your Silverado. It came from the factory with the standard 2" receiver and yours should be no different (though always double check). I use a 2" hitch ball. My GVW is under 1800 lbs, total length closed ~ 14feet, and you don't even feel it, no need for a sway bar. The only thing that I changed since starting out was replacing the hitch w a 2" drop to an adjustable height ball mount (MaxxHaul 70067 8-Position Adjustable Ball Mount - 5000 lbs. GTW Capacity) for under $20 because of that 2" drop + the slant of my driveway were too low to hook up the PUP in my garage.
Lots of good info here and nice people willing to help!
Welcome aboard!!