Maine Shooting Supplies

I have a ranch with about a half a mile long field leading up to it. I always seem to have unwanted animals coming up to my cattle like coyotes, bob cats, and even the occasional fox ( mostly when they are sick) but i am looking for a rifle to take them out. i also will be shooting squirrels and crows for some pleasure... i need a good smaller rifle (not a 7 mil or a 30:30) effective up to 200 yards.. i thought a .22 would do the job but apparently need more stopping power... any advice would be great... i always spends weeks at a time in the northern maine woods "roughin it" with limited supplies and will bring this rifle with me (originally carried my 12 gauge) and i also prefer remington or winchester..