RE: which 12 gauge
For 300 I would say a Benelli Nova, Mossberg 500 and the Remington 870 field grade. They are all pumps though. I don't know about getting a cheap auto. Sometimes you get what you pay for. The benelli has the smoother action of the three and I think it shoots 3 1/2 inch magnums if he every wanted to. The forearm makes a bit of noise though. And I thought it was pretty ugly looking, but that's just me.
I agree with saving his money. Use the 20 gauge for a bit longer and save up to get the gun he really wants like a guality auto or a wingmaster pump.
I don't know though, if the stoeger really has the internals of a benelli it sounds like a pretty good deal. I have a buddy that has a Franchi trap gun as well and it seems pretty nice. It's a 20 gauge. It is very light.
Good luck,
Paul