The shotgun is easy, because 12 gauge is what I have, now. I live in a region that is built-up if urban, and brushy/thicket/wooded if rural, so, many foreseeable shots are within slug range, and adding a rifled Benelli M2 or Remington 870 barrel provides me with a bit more reach than my current smoothbore barrels. I am probably about to add a rifled Benelli barrel, as it is. So, that means my rifle cartridge can be a .22 LR, which is chambered in a variety of firearms other than rifles, enabling me to “game” this one.
So, that leaves the handgun cartridge, and as I have stated on internet forums, so many times, my most-favored firearm, and most-favored handgun, is the Ruger GP100, because the original-pattern grip is a perfect for in my hand, the resulting trigger reach is perfect for my index finger, long-stroke DA is my most stress-resistant and least-perishable trigger skill, and, because I actually used my first GP100, with success, in a shooting incident, so that particular GP100 is not going away, ever. So, as much as I like several other handgun cartridges, my several GP100 revolvers use .357 Magnum. .357 Mag cases can be loaded to lower pressures, making them more tolerable in smaller-framed weapons. And, of course, .357 Magnum is chambered n rifles, so, I am gaming this choice, too.
Of course, I am basing these choices upon an economic/logistic scenario, and the factor that .22 LR is easy on my aging bones and joints. I shoot more .22 LR, through an S&W Model 17-4 K-Frame revolver, than anything else. My first handgun was an autoloader, a 1911, but revolvers soon dominated my handgunning, after I became a police officer during what was still the Revolver Era, and had to use a revolver in the academy, and during my rookie period. I ended up liking revolvers, too, very much. With my right hand aging-out of reliably maintaining a firm grip*, to enable reliable cycling an auto-loader, if shooting righty, and having problems reliably running the slide, if shooting lefty, well, if I have to choose “one” handgun type, going forward, it is the revolving pistol.
I also considered .375 H&H and .308 Winchester as my rifle cartridge, but then, .22 LR and .357 Magnum would have been competing for the handgun cartridge slot, and that would be a significant dilemma.
*My “limp wrist” malfunctions are more like “numb-thumb,” with limp ring and pinkie fingers contributing to a loose grip. My right hand has good days and bad days.