The front sway on most of these trucks is pretty decent. Adding a rear one is easy. I've used AddCo and Hellwig, found the Hellwig a little better as it didn't require that I drill holes in the frame for the bushing brackets...though the u-bolt style setup for them seemed like it wanted to slip under heavy use so I ended up tacking them to the axle tubes. It's been years so their hardware may have changed since.
As mentioned by dryslk some have adapted a Suburban rear sway to the pickup. That's a nice low-buck way to get there but the aftermarket bars are way fatter and really not expensive.
Tons of tire choices out there but for lowered trucks I always like to stick to a tire designed for sport trucks, generally you will find an XL load rating so that you provide for the heavier weight of a truck vs. most cars, and also in the event you might actually still haul something with it as I frequently did. Tire compound offerings still vary greatly in the sport truck tire line-up but depending on what size you go with there are more than a few sticky choices. BFG Sport Comp 2 are pretty decent and inexpensive to boot, don't last very long but reasonably sticky and some sizes are available in XL load. Toyo Proxes ST2 are decent too but not quite as sticky, good treadlife.
Oh, just put a set of Nitto 421Q's on my SS; they came practically new on a set of wheels I bought. Got a couple good reviews on them but I probably won't be abusing them the way I would on my old truck. This one is at stock height and the tire size is a little larger due to that.
Starting out by lowering the thing properly to begin with goes a long way. Proper rated drop springs instead of cutting springs, flip kit instead of pulling leafs and ending up with a mushy ride, etc.
Richard