Yes, what do you mean by "all around"?
Small game, such as rabbits, squirrels, quail, doves, pheasant, grouse I like a 20 gauge.
If you include waterfowl, and big game such as deer, pigs, bear, then I would choose a 12 gauge.
An "all around" shotgun, in my opinion, would be a 12 gauge pump with two, interchangeable barrels; a short slug barrel, 20-24 inches or thereabout, for the big game, and a longer barrel for the small game. That longer barrel of around 26-28 inches should have interchangeable, screw-in chokes.
My old Remington 870 meets those parameters perfectly (for me), but there are other brands also. Besides the pump actions, some of the semi-automatics also meet those requirements.
However, for most applications my own personal preference is for side by side double barrels. In general, a double barrel with 28 inch barrels is shorter than a pump or semi-auto with the same 28 inch barrel. It may be lighter, too, and a double certainly swings on target faster than the longer shotguns. But, it is all a matter of preference and getting used to your personal shotgun.
Anyway, a 12 gauge does it all, waterfowl, small game, and big game. What type you choose is your own personal preference. You just have to handle and try out all the various types in order to find what you like and what fits you best.
If you are a smaller person, a female, a teenager, or just smaller bodied, then a 20 gauge might be a better choice. A 20 generally has less recoil than a 12.
Oh yeah, shotgun "fit" is very important.
Also, either a 12 or a 20 gauge shotgun with a short barrel does pretty good double duty as a home protection weapon.