I was started at 9 years of age with a Winchester youth model .410 gauge crack barrel shotgun. Variety of loads, no recoil, small, light, teaches one shot hunting skill, must be manually cocked to fire, ammo is widely available and inexpensive, can be carried with action open, etc. Too many benefits or pros to list. That said my son who just turned 7 is being trained on a Remington 20 gauge youth model 1100 which is a semi auto, he just turned 7 but he is too big to for a youth model .410 at 75 lbs and 4.5 half feet tall. He shots the 20 gauge with no problem whatsoever and his favorite part is actually feeling some recoil he says it feels like he is doing something.
.22 caliber for squirrel hunting is a thing of the past given most shots are at squirrels in trees, if you miss that bullet is traveling far and wide so hunting tree rats with a rifle just ins't smart in this age of lawyers. 40/50 years ago it was cool and a good way to sharpen your markmanship but now with the movement of so many people out into rural areas and litigation based society we live in, the .22 for squirrel hunting just isn't a good idea. Too be fair like someone else said I was hunting with on my own with a 10/22 at the age of 11 but that was a different time. Now if you own your own land and I mean lots of it like over 500 or 600 acres of woods that are surrounded by other woods than go for it.