I started shooting with a .22 rifle when I was 5 years old. (I am 20 now). It was a Sears .22 semi with a 10 shot clip magazine. I put a lot of shells through that gun and we still have it.

I would look at just a single shot or bolt action .22 to teach the one shot one kill theory and then go to a 410 or 20 guage later.

I just went to Savage's website. They have a new youth single shot bolt action out. Here are the spec's.

Model CUB G Youth
Caliber .22 S, L, LR
Overall Length 33"
Barrel Length 16.125"
Weight 3.3 lbs.
Magazine Capacity Single shot
Stock Walnut finished hardwood.
Sights Rear peep sight, bead post front sight.
Rifling Rate of Twist 1 in 16"
Features Mini single shot bolt action, traditional safety, free-floating, button-rifled barrel, blued finish.
Suggested Retail $149.00

It will swallow even the .22 short, so your sons can learn at an early age and not even flinch using the shorts. CCI puts out a few loads for the short.