I was at the range today with my Remington 870 Magnum, in 20ga., with a rifled slug barrel with a cantilevered scope mount. I have a Leupold Vari-X III atop it, that is a 2.5-8X. The most accurate slugs I've shot are Federal V-shoks, with the "Tru-ball". (last time I bought them was 2 years ago, and paid $6.50/box). I was able to consistently hit a bowling pin swinging on a wire at 100 yards. Remington 870 is my recommendation. A great reliable gun that you can get all sorts of configurations for, from Youth stocks to home defense stocks, pistol grips, whatever you can think of. I went to the range in the past with over $200 in slugs ranging from $3/box, to $25/box, and what shoots best from MY gun, is the Federal Tru-balls. If you want to hunt birds, just pop off the slug barrel, and put on a bird barrel. Why would you handicap yourself with a smoothbore, when you can double your accuracy with rifling? I've had 4 or 5 Mossbergs over the years, and I just find them to be cheap guns. Cheap designs, cheap mechanics. I had problems with every one, and got rid of them all, and have not owned one in over 20 years now. I think they are only popular because of their price. Some older 500's are probably well made guns, but I will NEVER buy another Mossberg. Just pick one up at the store, and compare it to a Remington, Benelli, Browning, Savage, etc., and you can immediately see and feel the difference.
Don't make the kid try to hunt deer with a bird gun. Do it right the first time. The 870 in 20ga. is light, accurate, and has a good recoil pad. The 220 would be another fine choice. Get a dedicated slug gun. Forget the iron sights and make sure you can add a scope or a red dot. I personally love the Vortex Viper. Burris Fastfire is another fine choice. Bottom line is once you decide what you're going to shoot, put an effort into finding an ammo that will work well in YOUR gun, whatever the choice is. The differences are dramatic. I stay away from Brenneke, and magnums, as they seem to have higher pressures resulting in more recoil and less accuracy. You have to find what works in the gun you have. It won't be the same, even if your neighbor has the same gun. And practice! I was out practicing today, even though I haven't shot a deer with a shotgun in over 20 years. I'm a handgun hunter, and sometimes blackpowder. But I practice with ALL my guns so that if it's a rainy day, and I want to walk instead of stand, I'll take the shotgun. I want to know I'm able to hit what I aim at.