Re: 223 for Deer
A .223 might kill a deer, under the right conditions, with a perfect shot, if EVERYTHING works out right. If anything, and I mean anything at all goes wrong, you have wounded a deer that may take a week or more to die.
I could see starting an 8-year old with a .223 when your supervision can ensure nothing but a perfect shot will be taken. The justification is the balancing of recoil sensitivity against effectiveness.
Once a person is 10 they should be able to handle a .243, which is enough gun for whitetails in most situations. My daughter was skinny & had just turned 10 when she took her first deer with a .243. Adrenalin took care of any recoil issues when she was hunting & we used a LeadSled for practicing. I would STRONGLY argue against anyone 10 or older using a .223 on deer. It's not humane to shoot what is not expected to die quickly & with a .223 I don't believe you can expect all deer to die quickly.
As an adult you should be able to handle a .260 Rem or .25-06, which is where deer rifles start for most hunting situations. A rifle in this class will humanely kill a deer with a less-than-perfect shot & they have minimal recoil.
I am a fan of downsizing firearms in most situations & haven't carried a 7mm mag for deer in MANY years. That said, you won't see me carrying less than a .243 when deer hunting, and I don't believe others should either.