I bought one of my daughters and my son "starter" weapons for different kinds of hunting. Unless it's incredibly cheap, I think the "starter" deal is sort of a waste of time.
Kids progress so fast (both physically and as shooters) that it'll probably be a waste of money. Get him something he'll use until he gets old enough to buy something that he really likes and really suits him.
I wouldn't spend $1,500 on a Browning, but I'd probably opt for something step or so above an NEF single-shot.
If we were dealing with rifles, I'd say a good used .30-30 lever, or a good used newer model bolt (Ruger American, for example) if you can find one.
Since we're talking shotguns, I'd say a 12-gauge...a good, used, Remington 870 or a Mossy 500 (which would be a little cheaper).