Hunting Big Bucks

What size should I get?
I'm looking to buy a rifle, Remington 770, but do not know what size to get … Pests and Hunting like rabbits and coyotes on my property. Occasionally I quail hunt some food, and go big deer hunting with my friends. I was thinking either a 243 or 270 cal cal. I need a bullet that can kill something as small as quail, rabbits, coyotes and without causing much damage (I'd rather not lose them, so the skin of rabbits and coyotes) to bring down a large deer.
I would say a 270 because the 270 can still hunt animals like deer, mule deer, pronghorn, bear Black and wild boar.And to control pests that would buy a Ruger 10/22 i own one and it is best for pest control and small game.
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