I would think that 10mm would be a bit weak, if responding to a large brown bear in the house or an irate moose attacking cars; as both incidents happen on routine
Glock 20 in 10mm for #2 and #3. A properly loaded 10mm is equal to or better than a 357 and both are closer to 44 mag than most understand. Any handgun that offers significantly more power is going to be significantly larger. For me at least once you get to a revlover larger than 4", I'd just as soon carry a rifle, and you'll need at least 6" of barrel from a magnum revolver to better a 10mm.
For pure hunting this is where a long barreled 44 is about the minimum and the hand cannons, 454, 500 S&W etc., have their place if you insist on hunting with a handgun.
For LE, I'd not want a handgun much different than what were used most anywhere else. Any quality semi or revolver someone is comfortable with. I would however insist on a long gun in the vehicle capable of dispatching larger animals if needed. A Ruger All Weather in 30-06 would make a good choice I'd think.