I think you should let the kid decide , which is what I did with my 2nd son.
My oldest son (15) isn't much into going to the gun range anymore , he is more into archery ( recurve - his choice ), which is fine. We shoot archery on the side of the house ( 20 yards).
My middle son (8), I let him decide what he wanted to shoot. I took a Colt Semi-auto pistol with a red-dot , a Marlin 700 22 rifle with irons , a Ruger 10/22 with Tasco 2.5 -10x scope , a Savage 22 Bolt gun with Mueller APV scope and a S&W J-frame in 22.
At first he wanted the 10/22 , so I modded it to fit him with a shorter stock. After a few months , he switched to the bolt gun (Savage GVXP ) and now loves that the most. And changes back and forth between shooting my Savage , and my dads 77/22 with a can or dad's Marlin 17HMR. However during a 3 hour range trip , he will shoot em all , including my dad's FA Vector Uzi with a 22LR conversion.
Arguing that the a kid should start on iron's is like saying that have to start on a bolt action , or on a revolver. There is no set rule.
Whatever you do , make it enjoyable , dont be a range nazi , dont "bark" orders at them , dont be dissapointed if they mess up , dont get pissed if they dont shoot well. Let them enjoy it. The point is to teach them safety & keep their interest. Not every kid wants to be a sharpshooter , some may just being at the range with dad ( or mom ) and sharing in something you enjoy.
It was only after a few months of shooting ( twice a month ) , that we were both laying prone , shooting our 22 rifle at the little spinner ( chicken ) at 50 yards. Lil whipper snapper hit it 5 times in a row , and said " beat that ". From there it was on , we went 5 strings of both of us not missing , somehow on the 6th string I must have pulled my last shot
, and he won...hehe...funny how that happens.
Now each time we are at the range , there is some fun challenge , that he comes up with , it could be the steel targets , clays , poker chips or paper.
He brings a target home from the range each time to show his brothers and his mom , as well as anyone else who visits us.
He is wanting to shoot the AR , so I am swapping out an entry stock for the full A2 stock on my A2, which should make it fit him fine for the bench.
Now while watching movies , its enjoyable to hear him criticize the shows regarding firearm safety and do's and don'ts.