Mtncows
You mentioned ride and sway
For the sway make sure you go with the Load Range E heavy ply tire, the stiffer the side wall the less sway, would not be surprised if your truck has Load Range C tires most people just don't want to spend more money on tires.
With ride one of the way to improve that is to go with a BF Goodrich or Michelin these 2 brands are cosistanley ranked for ride quality, but Range E tires will not ride as good as Range C, also the more aggresive the tread the poorer the ride quality and the more vibration wich leads to front end repairs (tierods, bushings, bearings etc...).
From my experiance no problem with adding the wider tire to the stock rim, the problem starts when you put larger tires on aftermarket rims and don't properly calculete rim offset.