The biggest hand cannon you are comfortable shooting. I would assume you would be fine with a good full frame 45. My wife who is not strong and never a gun nut is deadly with ours.
I am a huge fan of the FN 45. 16 rounds, not much kick and it is SA/DA. So you can store it decocked and the first shot is a long trigger pull DA. So really safe in the nightstand. Then the second and on is single action, quick short pull.
But there are tons of good guns out there. It boils down to what feels good in your hand.
For the rodents, depends how far away. A small bore rifle like a 22 if they are far. Shotgun if they are close. Nothing wrong with an AR either for that. And you are covered for zombies.