Having grown up on a farm we've had to deal with a variety of critters. The Ruger 10/22 was always a good choice along with the 12 gauge pump. If it wasn't close enough for one of those, coyote bothering the cattle, etc., the Remington .270 (zeroed at 200 yards) worked real well. Always wanted a pistol when I was running a trap line but Dad didn't think "kids" should be have one. Got him a Ruger Mark III when I got mine and he's used it more than once on critters, primarily raccoons.
Since you already own a Mossberg 500 I'd suggest getting a second one due to the fact that the safety and all operations would be identical to your defensive one. Consider keeping a headlamp with it. The LED one's have a good distance and features plus where you look the light goes. A light pipe on the barrel is always a good choice since you may be in low light situations and should work well with the head lamp. A mounted light is your choice. I'd suggest loading it with #4-5 shot. A stock sleeve with extra rounds is also nice and you could carry something heavier in the occasional case that what you're shooting is thick skinned or hard to take down. Keep in mind that some critters operate in pairs so extra rounds are nice to have on hand.
I'm partial to a Ruger 10/22 with either the standard 10 round drum mag or 25 round mag but feel free to go with what you like although I'd strongly recommend that you go with a semi automatic. A scope similar to Cabela's caliber specific would suit you just fine. The .22 is nice in case your dogs are in a fight and can't/won't separate from the critter or you happen to be able to step on the neck of the critter during the fight. That way you can place your shots carefully and not worry about multiple projectiles like a shot gun and not worry about shooting your dog or foot.
The .308 is an option for critters out of range of a 12 gauge or .22. Not sure what kind of sight picture your scope has but some practice at a known distance range should help you figure out where to sight for 100 or 200 yard shots.
Hope this helps.
Walt