The thicker stuff is nice as its not as affected by concentrated heat.
Stainless looks nice but they you get spatter and have to dress it with a flap wheel and that's probably going to be a sad day.
If you can get HRP&O (hot rolled pickled & oiled) they previously remove the mill scale which makes it just a bit nicer. Looking at my Alro catalog, A36 HRP&O is only available up to 1/2" thick.
Many steel yards have processing via flame cut, shearing, laser or waterjet. Depending on thickness the shear can put a curl into the metal via the stresses imparted during the process. Laser would be my choice if they can do the thickness that you want.
The first steel bench I made was 5/8" thick and I had them ship the "drop" after shearing 8" off a 48*96 to get 40" x 96". I made that drop into several more useful things over the years.
Just also had a thought that you might be able to find a 36x 120" as-is at the steelyard, no processing needed. Alro stocks that size in several thicknesses. Looks like up to 7ga in the 36*120 size, just shy of 3/16" thick.