for squirrels that are gonna be shot at running, use a 12 ga semiauto or pump, use no. 7 1/2 to no. 5 shot. but only use shot over six at 30 or more yards because this will tear the squirrel apart. 2 3/4 shells will work fine, no matter the shot size. anything out to 30 yards use a skeet or improved cylinder choke. any more than 30 use a modified or full choke. for still hunting, i would use a .22 lr, .17M2, .22 mag, or .17HMR, in any action (preferably semiauto if legal). they are only about 100 bucks at walmarts and bullets are cheap also. like 11 bucks for 550 .22 lr bullets. also top it off wiht a scope that can pull in enouhg light to shoot near the end of the day. for coyotes if you want to keep the pelt try only headshots (unless you want the head with it) and make sure your gun is super accurate and use the lowest grain bullets u can find. they will probably go faster and shoot flatter. but if u want to hit its vitals try somthing like .22 mag at the least, .22-250 (definitely not in ranges at 200yds or lower because of power), .223, .220 Swift (i prefer this one), .221 Fireball, .218 Bee, or maybe even a .243 at most. you can find plenty of info on how to gut and everything all around the web. u can choose any action u want but just make sure you top it of with a red dot scope or soemthing with some kidn of light if legal. good luck.