I think you got a few years before a shotgun. At 7 he sould probobly learn gun safety and sportsmanship first, this could acomplished with a BB Gun.
When he gets old enough and mature enough to handle a real gun. I would suggest a youth model 1100 in 20 gauge.
This is a gun that he can be succesfull with and at the same time has 1/2 the recoil of a pump.