Aside from traction depending on what terrain you will be towing on, tires are not as critical as people seem to think.
Un-like a pickup truck loading items in the back OR possibly your Expedition loaded inside and on top, where side wall and load rating come into play, towing requirements stipulate that the tow vehicle should only receive lateral load from the trailer and the downward loads must be little to none in comparison. That is why most all hitches on average have a max tongue load of 600 lbs.
Be sure to get load range E tires. Max pressure 80psi.... When you're not towing, leave factory recommended air pressure in the tires. If you're towing something heavy, bump all 4 tires up to 70-80 psi. That will give you the stiff sidewall you're gonna want.
I used to be in the Goodyear silent armor bandwagon. Now I rock Michelin Defender LTX mud and show rated.
If you're towing something heavy, the tires make a huge difference. I tow a 7000+ lb boat over 1000 miles each summer and the rear end was a bit squirrelly even with the sway bar upgrade until I put better tires on. Switched up to XL rated tires on factory 20" rims and it is as planted as towing with my pickup now. I probably could have gone up to the E rated tires for the trailer weight, but the XLs give a little softer ride when unloaded.
With an independent rear suspension vehicle, there is no way you need load range E tires. Thats complete overkill. Sure it will help, but the sway is coming from the suspension more than the tires. Get the rear sway bar swapped for Hellwig to start with.