There are four serious handgun cartridges:
.22 Long Rifle -- everyone has to have a .22 pistol, for practice, targets, plinking, and hunting.
.38/357 -- these are really the same cartridge, since most .357s shoot .38s very nicely. This is perhaps the most versatile handgun ever developed.
.45 ACP -- THE defensive handgun cartridge.
.45 Colt -- properly loaded in the right gun (like a Ruger Blackhawk) it is fully the equal of the .44 Magnum
You need three rifles:
.22 Long Rifle -- same reason as you need a .22 pistol.
A "varmit" rifle -- from .22 Hornet to .223 Remington. If you are a serious varmit hunter, you probably want a "heavy" varmit rifle in a hotter cartridge.
A high-power rifle -- As Townsend Whelen used to say, "The .30-06 is never a mistake."
You need one shotgun -- a 12 gauge pump with screw-in chokes.
If you're into various games and sports, you'll need guns tailored to those games -- but the 8 I've listed here will do 99% of whatever needs to be done.
That's my story, and I'm sticking to it.