The shotgun has a wide variety of loads readily available. Because shot is spherical, it tends to lose velocity rather rapidly. Since it has no spin imparted to it, an individual ball does not necessarily fly straight and true for very long. The more choke a shotgun barrel has, the more it helps cluster shot at a greater distance, the less choke the greater the dispersion.
Despite all the shot sizes, types, and brands available, all the shotgun shells I have were manufactured by Remington. Other companies have good products, but Remington, and especially Remington "Nitro Express" loads, are simply what we have always used, and I have never had any reason to change. Green is a good color. If checked the green boxes I have, you would find some rifled slugs, some 00 buckshot, some #2 (not buck) shot, some 2 3/4" #4 shot, a couple of versions of 3" #4 -- one regular Express and one copper-coated and buffered Turkey load -- and finally some #8 shot.
If I were going turkey hunting, I would put on my vented barrel with a screw-in Extra Full choke and load it with 3-inch #4s. If I were going after deer, I would use my 18.5" barrel with rifle sight, and I would load it with slugs. For doves, I would go with the longer barrel and, depending on the situation, screw in a full or improved cylinder choke -- since I don't have any #6 shot, I suppose I would have to use #8. Theoretically, my #2 shot would work for geese but steel is required most places. In practice, I use the #2 shot for coyotes, again with the extra full choke.
Buckshot, as far as I'm concerned, is mainly a home defense load. All the experts recommend it. It will certainly work. I have a couple of 3" 00 buckshot rounds in the shell-holder on my shotgun's stock. But in the magazine, I have #2 and #4 loads. That's because I use my 870 for pest and varmint control at night. There is no sense wasting a load of buck on an armadillo digging up the wife's flower beds. Also, because I am not an expert in these matters but having seen many coyotes sent to their rest, I have always thought that a load of #2s at household distances would be discouraging to two-legged varmints as well.
I was out the other day fooling around with the 870 in short-barrel configuration. This barrel is choked Modified -- which means, despite its short length, it is supposed to keep roughly 60% of the shot in a 30-inch circle at 40 yards. Just for reference a Full choke is supposed to put 70% of the shot into the same area at the same distance, an Improved Cylinder does 50% and a Cylinder bore (no choke) does 40%. A Skeet choke puts 50% of the shot into a 30-inch circle at 25 yards, which is good for skeet, I guess. A Super/Extra Full is, as expected, even tighter than a Full and, with the proper loads, is used for head shots on turkeys out to 40 yards. You don't want to pick a lot of shot out of your turkey breast.
As it happens my short Modified barrel handles Remington rifled slugs quite nicely and enables me to hit consistently at ranges between 50 and 100 yards.
Back to my main point, I was fooling around and decided to test the penetration of #2 shot on a relatively hard object. In this case, a chunk of cedar about three or three and a half inches in diameter. I cut this cedar down a couple of months ago, so it is dried out a little. This is what the front looked like after being shot with a load of #2 Nitro Express 2 3/4" 12 gauge with a Modified choke from 10 yards.
I would call the vertical spread about six inches so the little log caught a good portion of the load.
What surprised me was the back side.
Now this cluster of shot did not penetrate three inches because it is on the side, and it did not go through much of the red heart wood, but it still got through. Below is the sapling my cedar chunk was leaning against.
I'm pretty sure that a load of 2s at across-the-room ranges would ruin a bad guy's day. Number 8 shot at very close range could prove fatal. The smaller the mass of the individual projectile, the faster it dumps energy. Take that cedar chunk out to 20 yards and not only would fewer pellets strike it, there would be a lot less penetration. At 25 or 30 yards, buckshot, with its greater mass, is a better choice if you need more penetration.
The thing about shotguns is that everybody is always right and always wrong when it comes to shot choice, loads, and chokes. It all depends on the conditions.