AA's are the gold standard. The gray hull variety are know to have "slick" hulls that work well in auto loaders and box feds. Down side is they are fairly expensive.
I've been using these federals for about a decade, you can get them in loadings (hot to mild) to match what you are doing. The ones pictures below are a heavier load that will run anything and I've never had an issue with quality. Really nice thing is you can find them for $5 to $6 bucks a box.
If you running a box fed most gamers chamber check all their rounds for matches, they also tend to run really hot ammo. Keeping most open shotguns running is a labor of love (and curse words lol).
Most serious 3 gunners will game what shells they are using. Hot shells for longer targets, lighter stuff for clays and close knock overs and may even throw in spreader type rounds for really close up clays . I'm guessing running a stage with steel knock overs at any range will give you some frustration with the light loads your using. You'll want to have a good idea what your guns are patterning with the load/choke your using especially if you using a SBS. I have a 12" 870 and even with a full choke it doesn't have nearly the pattern / range as my full size guns.
For slugs you see primarily low recoil 1 oz or 7/8 oz loads. Fiocchi offers both, the 7/8 oz load has less recoil than a shot shell and may require some tuning to run in many guns. I'm currently using their 1oz load with good results. Shotguns can be finicky with slugs, my advice is to get a couple boxes of each, see how they cycle, see how they print and make your decision from there.