For the house, a shotgun. Remington or Mossberg. Pump or semi-auto. 12 gage, or 20 [if someone using it is recoil averse].
Hunting: Depends on what you hunt, and where you hunt it [In a lot of New York, you can only hunt deer w/ a shotgun]. Northeast Whitetail, try a bolt action 7mm-08, .270 or .270 WSM, a.308, or .30-06 [Remington, Winchester, Ruger, Browning], or if you like levers, Marlin or Mossberg in 30-30, or Marlin in .308 Marlin or .35 Remington. .338 Federal’s good, too. All the 30s should be OK for blackbear.
For moose, heavier. Ditto for Elk [ I’d start at .30-06]. Ditto for boar and double ditto for Brown Bear [think 300 mag, 300WSM, 338 mag, maybe 45-70, .358 Win.
Small game: .22LR, 22 masg., 22-250, w/ 25-06, .243 Win.
Good luck, .223 works for varmints, too- like coyotes. Good luck.
Hows that work out for you do you have to buy special shot to shoot a deer?