There really isn't one shotgun great at small game and ducks. Sure you can get buy with one that does, but orient your purchase to one or the other, not both. Ducks usually mean semi-auto's in 12 gauge and small game is best with shorter and easier to handle break barrels (singles, SXS or O/U's)... in my opinion anyways. There's nothing wrong with an inexpensive break barrel single shot for a young hunter and probably the safest to learn with as well. (I still prefer using an old single shot for small game over my pump and O/U due to it's compact size, extreme light weight and quick pointability for quick shots up close.)
As for the gauge, a lighter easier to handle 20 is far more pleasant to shoot, especially for a young hunter. You don't want the kid to cringe everytime he pulls the trigger. Also, the 20 guage slug kills pretty much anything.