Depends on three factors. Weight of the load, velocity, and operating system of the shotgun. Like Locutus, I own an M4, that will digest almost anything, and several gas operated models come with an adjustible gas system these days. you can set it for goose droppers, or light field loads, and can be used for taking down a bear, ot a round of trap.
Recoil operated, that's a whole different can of worms, and you usually end up trying out a few different options, before you find one it likes. And if you have three, you might find that they like 3 different loads, or one in particular, that all 3 like.
For instance, my grandfather's 11-48 takes a stiff push, to cycle, and does best with slugs, from Winchester, but chokes on their 2.75 #4 and #6 loads. 4 or 6, Federals all day long. Remington 00 Buck, zero issues, any other brand, one hang up out of three loadings.
My SPAS 12, unless it's buck or slug, it gets switched over to pump, because, with the exception of turkey loads, the bolt might move about half way.
My M4 and my wife's Versamax, they don't care what you feed them.
Dad's 5500, pretty much the same, as long as you keep it clean. it gets dirty, it will run a few target loads, then start hanging up. Field loads will knock it loose again, and zero issues with slugs or buck.
When you go looking, might sound odd, but look into the used market, for someone upgrading. See what they ran and how well it worked for them. I got a smokin deal on that SPAS 12 because it needed a serious, sent to a local smith, cleaning, and the guy was getting rid of it because it wouldn't cycle bulk target loads. Something the shotgun was not designed to do, on semi, from the factory, and he didn't know it would go pump. Value at the time was around $1,500. I got it for $750, because he thought it was broken.
Myself, I'd look for a Versamax or a Mossberg 930, used or new, for reliability. Same with older 11-87s, or Mossberg 5500 Makr IIs. 5500 and 5500 Mark I models had a stiller recoils spring, and tend to need a fair amount of lube, to function with low pressure loads.
