All a lowering kit is is springs for the most part. Usually the coils are packed closer together to allow a drop, some cases they might even be lighter sprung. If your changing springs it's a good idea to do struts. If your struts are old, the sudden extra compression from a drop will make them go bad if they weren't before. Add a camber kit and anti-pogo kit to your list of things to do.

Link on the GMPP handling kit doesn't work, just it consist of sway bars, strut tower bars, and rear trailing arms. Add another strut tower bar for the rear and you're golden. This kit will do the most for handling, period.

Subframe connectors? Sway bars tie the control arms to the subframe and thus car. They prevent chassis flex/lean while taking corners. The thicker the bar, the less it lets the car lean. Trailings arms are just structural items for control flex in the rear suspension. Tubular ones are a lot stronger than the stamped ones from the factory.