If you go with the BB gun, make sure that he understands that it is not a toy.
The cricket is a good choice. I all ways wanted the Ithaca single shot lever action. It sold for 19.95 through an add in Boys Life. You won't get one for that now.
Every one should start on a single shot. I believe that it improves skills knowing that they have only one chance to hit the target.
PS dittos on the hearing protection. Young ears are more easily damaged than adult ears.