It's really not about what action you use, so much as the gun's handling characteristics. I have no love for pumps, but a heavy, slow-swinging semiauto won't work any better on quail than a heavy, slow-swinging pump gun. Neither will a heavy, slow O/U, or a heavy, slow SxS. And in the steel-shot world, a 28 Gauge SxS, while it might be the ticket for Western Quail in heavy brush, isn't worth a damn on ducks, to say nothing of geese!
Doves can be shot with nearly anything, since hunting is usually stationary. If you are walking around, though, a light, quick gun is only way to go. Doves sure don't always fly straight, so a quick, light gun can be of value even when you're hunting from a chair. People do, however, bag some doves every year with their goose guns.
However, if you're hunting Western Quail and Chukar, don't plan on getting on target with a 12 Gauge pump. Slow guns and fast birds don't mix. If you don't have a good pointing dog, that's goes double. No, triple. By the time an 870 Express 12 Gauge goes from carrying to your shoulder and pointing at the quail, the quail is behind the next bush or rock.
IME a 12 Gauge pump gun is a big mistake to use for any of that hunting. I bagged all of those birds this past season, BTW, so this is not mere speculation. Only one (a single quail) was with a 12, it was incidental when my dog flushed out a covey of California Quail when we were looking for Pheasant. I took 4 shots to hit a bird in that fast-moving covey, and the gun I had was a semiauto that weighed 1/2 lb. less than my 870 does.
Now for ducks and geese, 12 Gauge is standard. The decent ammo that doesn't cost too much is 12 Gauge. Serious waterfowling is done with 12, and sometimes even 10 for long shots on geese. Carry weight and quickness aren't real factors; a heavier, slower gun can be best on waterfowl, that move differently from small, fast upland birds.
The bottom line? You probably ought to decide first, what you want to hunt most, and get the appropriate gun first. A 6-7 lb. 20 Gauge of any sort is where to start, for those upland birds. A 12 Gauge heavy enough to be kind to your shoulder is the starting point for the waterfowl. Pheasant and duck guns overlap, but quail/chukar and duck/goose guns generally don't. Beretta has done their level best to make a true all-purpose gun with the A400, which is a 12 Gauge that weighs well under 7 lbs., shoots everything from light target ammo to 3.5" goose and turkey loads, and can be had with a shock-absorbing butt so you don't blow your shoulder off with the latter. But it sure ain't cheap, and for the money I probably would rather have two guns, tailored for their purposes.
This is not some sort of "gun snobbery", BTW. It comes from my experience trying to hunt these fast upland birds in the high desert near the Mexican border, with a 12 Gauge 870. It convinced me only that I needed to get a different gun for that sort of hunting -- just like a .22LR isn't a great deer gun, nor a .375H&H the best choice for cottontails.
