Everything counts and it all adds up. Anyone can get hurt by recoil, muzzle blast or the scope.
There are various ways that the recoil or force can hurt us. One way is from crushing the flesh and a soft pad is wanted.
Far too many guns have hard butt plates and most of the old recoil pads are way too hard.
Then there is the force that zooms the body backwards and might even cause the gun to jump from the youths hands. All this is a proportion to the weight of the gun, the force and the size and personality of the youth.
To get more specific say away from old 30-06's! The cartridge is much too powerful for small kids and most of them are old guns with way too much drop at the comb. A straight butt stock will kick much less than one with drop.
An expample of the best stock, in my view, is the Kimber 8400 Montana what with its minimal drop at the comb and soft Decelerator pad. This rifle is for example only for its stock and pad design. The rifle itself is chambered for cartridges that are too large.
As to cartridges the 243 might be a place to start.
The gun must fit the youth. A short LOP must be done or who could hit anything with a gun thats too long. Finally I like a three position safety so the kid can unload the gun, keep the bolt handle down and be on safe. All three are necessary.
You want to work your way up first with a .22 and always with ear protection. Make sure most of all that the kid never gets hurt. Then with reduced loads and finally with a load that will not kick the most.
Ruger has a compact model 77. We know autoloaders kick less but I would not want my kid to start with one and he did not. My son started with a Kimber 84M Classic 7mm-08 with light handloads and even now at age 30 he shoots the 120 gr Ballistic Tip.
Ruger Compact
