My father was a hunter, and an NRA rifle & pistol safety instructor. Mom plinked, and shot pests. She was a crack shot with her JC Higgins .22, and pretty good with her Ruger Bearcat.
Learning began about the time I was big enough to hold one up. My 14th birthday present was my very own Winchester .22. At 16, Dad gave me a Remington model 600 .308 and at an auction, bought me a Winchester Model 12, 12ga.
That particular .22 is long gone, but the deer rifle and the shotgun I still have, and they have lots, and lots of relatives keeping them company these days.
All else being equal (and it almost never is) bigger bullets tend to work better.