Every weapon has weaknesses, so the most important thing to do is to decide which job is most important in your particular situation.
Some weaknesses-
Big bore handgun- limited range, difficult to shoot well
small bore handgun- very weak on large game, limited range
.22 rifle- weak on large game, placement critical
military style semi-auto rifle- heavy, not versatile load choice, bad for edible small game
Shotgun- heavy ammo, limited range
Combo guns- single shot, heavy
After thinking about this dilemma for several years, I have settled on an answer I like, but it probably makes sense to explain the reasoning I used to get there. Also, I understand that other people in identical circumstances might make different choices AND be very successful with them.
The areas that I find myself in most often include typical Mid-western farmlands and woodlots, Northern conifer and mixed conifer-deciduous forests, and Southeastern lowland hardwoods and swamps. Because of the amount of time I sped there, I am most likely to need a firearm for long-term use in the big north woods. This environment can provide both large and small game (as can farm country and swamps) ranging from black bear and moose to grouse and red squirrels.
After considering what one gun would best serve me for LONG TERM foraging, I have decided that I really need two guns to be most effective. The first is a bolt action, center fire rifle chambered in a traditional hunting cartridge. I prefer a .30-06 or .308, although anything from 6.5mm to .375 would work. I want the action to be a military style if possible- preferable a ’98 Mauser or a derivative. I want the stock to be synthetic, and I want a simple scope (generally a 4X fixed) mounted in Weaver rings and bases. The rifle should have fixed sights, best if the rear is an aperture, and even better if this is part of the rear scope base. It should have a simple sling, and the recoil pad should be removable to allow a few spare parts (extra screws, firing pin, etc) to be stashed in the butt.
This rifle should be consistent able to place 3 shots into no more than 2” at 100 meters in the field- and better than that is nice. It should function in poor conditions (this is the goal of the military action) and be portable. It is simple to enhance this reliability.
The ammunition for this rifle will be loaded with a moderately heavy for the caliber controlled expansion bullet. The .30 cal 180 grain Nosler Partition is a fantastic choice. It will be sighted to allow good hits reliably to 300 meters without making short-range shots tricky- let’s say 2” high at 100 meters. The goal here is to kill things from the size of a beaver to a moose with little fanfare. IF a reduced load can be found that has a usable point of impact at 25-50 meters, it will be included. Something like a 115-180 grain cast lead flat point at a velocity of 900-1300 fps will work nicely on small game.
The other gun is a small handgun- either a .22 rimfire revolver or self loader or a centerfire revolver chambered in anything from .32 S&W to .357 magnum. This gun has to be portable and shootable. I need to be able to group less than 3” at 25 meters ideally. This gun will be for small game targets of opportunity while I am engaged in activities other than hunting. Have you ever had an opportunity at a rabbit while hiking, or at a porcupine while looking for firewood?