I've had good luck with Winchester 3" 1oz 1760fps (15rd white box), and PMC 2¾" 1oz 1600fps.
Those Winchester shells will rattle your teeth, and hit deer somewhere between a freight train and semi-truck. They will also knock over my 12x20" steel targets at 35yds.
Yeah, they don't really expand, but when they cut a ¾" hole clean through a deer, they don't get very far. I strongly suggest you take broadside or quartering away shots. That slug will drill a straight line through the deer, so if there's guts in the path, it's going to be nasty. When I learned this the hard way, it about jellied the shoulder, definitely jellied the heart/lungs, and had guts coming back out the shoulder by the time it fell in 10 yards. Had the ground covered in blood.
If you have to take a head on or quartering to shot, aim for the neck so the pass through goes over its back and not in the guts.
I zero the RMR (9moa dot) on my 590a1 to have the shot group centered on top of the dot at 50yds. Hold center mass out to 50, and beyond put the top of dot on their back. Accuracy drops off around 75yds so that's as far as I'll hunt with it, but can hold a man-size target out to around 125yds.