squirrels: I use only my .22lr, bow, or pellet gun just for the challenge, my .22 is a ruger 10/22 w/ 4x scope on, i just sit and wait by some oaks or hickory trees

rabbits: I use 12 or20 with my dogs (beagles) depending on the area i am hunting say i am hunting in willows or canary grass i will use my 12 for better penetration through the thick stuff

pheasants: i use my 12 or 20 depending on what i feel like bringing when i have my beagles. with #6 or #7.5 6 i found is better

yotes and fox i go with a hunting party with dogs and use 12 gauge buckshot or my uncles .223

i have beagles trained on rabbits, pheasants and not squirrels just because them squirrels are a nusience and if i see one in the woods while i am doing any other hunting it will drop and train the dogs not to after the squirrel but then sneak it into my vest

good luck