My thought is that a 9 year old should be shooting only a single barrel gun. Maybe at 12 something else. If you have him shooting, let him shoot cans or whatever on the ground. Not things, at least , when he constantly misses. Maybe a good first experience is taking him to a private area and shooting a 22 rimfire at some inanimate objects. Then you can teach him about gun safety and he can become comfortable with guns firing. Also, the single barrel should not be one with an outside hammer, that is too hard for his young hands to cock and handle. BB guns are wonderful trainers and just as fun for the shooter as any others.
I have to agree with Daryl about starting a kid with a single shot. A repeater, even a sxs is just too much responsibility too fast.
As far as what single shot to begin a future double-gunner on; I suggest the Savage Model 220 with no external hammer, and a slide safety to learn with. The changeover to the sxs will be seamless having learned on the same mechanism. The 220s are readily available on the gun sales/auction sites.
As for guage, I have mixed feelings. I started my boys with 20s because I remembered experiencing the disappointment of not being able to take game reliably with the .410 I started with. The 20 was too much gun for my boys at 8 or 10 so I guess it depends on the boy. If he can handle the 20 I'd go with that, if not, then the .410 certainly is an improvement over a Daisy air rifle! It may be that with reduced recoil loads available now, guage doesn't matter so much. Just my thoughts...Geo