The H&R single shot is one heck of a great value for it's money. I own one with 4 different barrels. I can hunt deer with the rifled slug, birds with the interchangable choke smoothbore, rabbit's and squirrels with the .22lr, and coyotes out to 250 with the .223 bull barrel. Face it, your little boy is only going to get good if he practices and you can afford him doing a lot of practice with the .22LR. The single shot is going to teach him to make every single shot count. He'll apreciate that when he's older.
Don't worry about the 30-30's power. It's got plenty for any deer you'll ever meet. I keep telling people that it still has more energy at 300 yards than a .357 magnum pistol at the muzzle.