I use 3/8" AR-500 material, which will resist deforming very well. We've shot it with 210 Bergers from a .300WinMag as close at 100 yards and the marks spray paint right off.
We've hit it repeatedly with a .338 Lapua, which, while not damaging the surface layer, eventually causes a little dishing of the plate. This is not dangerous, but does increase the size of the splash marks, so when a plate starts to bow a little, we just flip it over and shoot it form the back awhile.
I've had it shot at 1k with a .50BMG, which doesn't damage the surface, as a rule. It does bend the plate rather quickly, but the bigger problem is that even .50BMG "ball" is often not pure lead core. A "ball" round with the sintered steel core one often encounters WILL damage the hard surface layer, even at 1,000 yards.
Many commercial targets use 1/2", and if I were running a range where I'd get a lot of wear and the plates are a little smaller, I'd go to 1/2".
As it is, at over $1,000 for a 4x8 sheet, the 3/8" is expensive enough. Since steel is sold by the pound, 1/2" is proportionally more expensive.
Also, 1/2" is proportionally heavier than 3/8", and my 24 x 33 torso-sized plate is already 85#, which is getting to be enough trouble to haul up the berm at Quantico. A 1/2" plate the same size would be over 110#.
Something worthy of noting is that extremely high velocity bullets, such as those at over 3,000 from a .223, etc., will pockmark the surface. Since all of the "AR" series of steel is merely "Abrasion Resistant" and only surface hardened, if a lot of wear like this is anticipated, the 1/2" is going to hold up longer/better because the hard layer is a little thicker.
The SS109 bullet, as well as the steel jacketed bullets one finds in much of the commie calibers and stuff like Turk 8x57 is very hard on the plates, and dangerous to shoot. It chips the surface layer and steel-on-steel impact allows the bullet fragment to retain a LOT of it's initial velocity.