When I bought my last set of tires, they mistakenly installed the 265/75-16 instead of the stock 255/70 tires that I wanted. I didn't check before I drove off, but I noticed that the truck seemed bouncier and floated more. At first I thought it was just a softer sidewal since I went from the A/T Bridgestone Revos to the highway all-season HL Alenzas. I looked at the tire size and immediately went back to the Firestone store and told them to change to what I wanted. They didn't have my size in stock, but changed out a few days later and I'm happier with the stock size because I like how it handles. I have the 01 Sport Trac, which should be the same as the Sport, so they should fit.
If you go with taller sidewalls, it will change the handling if that's what you want. If you want larger diameter tires and stiffer sidewalls, you'll have to go up a rim size. Taller sidewalls will be better for offroad to absorb bumps. It just depends on what you're preferrence is.