The recoil and report of the 357 with the IMR 4227 loads i worked up were a joy and would do well at 40 to 70 yards , stick to soft points if you dont reload ..heavier the better
But at 11 i would say consider the 44 mag not a man here in these handi forums can live with out that old trusty 44 ..
Been using it for years , recoil is quite mild and reaming the barrel isnt a worry ever

I bought my oldest nephew a super lite youth in 243 and accuracy has been good ( he is a lil scawny 10 now) and it pushed him around a little at the range , so i worked up some reduced loads with a good 80 gr bullet .. Happily same point of impact .. And my thinking was the same as yours something tuff that can hold up to a young mans first rifle and also can be upgraded in the future so that he shouldnt need another hunting rifle till he is ready to buy his own .. or atleast pitch in some money to get into what he wants next ..
But my hopes are that his youngster gets that rifle one day,
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