Although this is in the shotgun section, I was started with a single shot bolt action Remington model 514 .22 rifle when I was big enough to hold it up to aim. By the time I was 6, I was trusted enough to keep it in my room, and take it to go groundhog/squirrel/rabbit hunting, or if a fox or stray dog got after my mom's laying hens. I firmly believe a person that is taught with a single shot will be a better game shot than if they had been started with a repeater such as a semiauto. They KNOW they only have 1 shot, so they'll have the perfect shot before ever pulling the trigger.
I taught my own kids with single shot .22s (Chipmunk & Marlin 15Y), and have taught too numerous to count kids over the years as instructor. When my son carried his rifle after tagging along with me squirrel hunting, I carried the .22 ammo, and when he not only spotted the squirrel, but also showed me he had a safe shot with backstop (tree or hill), I'd hand him 1 .22 LR round. He got 4 squirrels with 4 shots his very 1st hunt. My daughter same thing but she was using my favorite 7mm08 (hers since then), she got 2 deer with 2 clean, 1 shot, drops.
My most useful & deadly firearm for hunting after I started getting more firearms was a Savage model 24 DL chambered in .22 mag over 20 ga. If I saw something sitting, the .22 mag (with solid or FMJ on edible small game, HP for coons, groundhogs, and varmints) would be used when sitting still. If it took off running or flying the 20 ga barrel would be used. I would still have those guns if not for the house fire.