Pheasants
Grouse
Chukar
Quail
Dove
Ducks
Geese
Rabbits
Squirrel
Deer
Clays of any size (although I dearly hate rabbits)
Angus Lincoln - A 12ga is fine, as long as the kid is strong enough to operate it. The recoil can be mitigated by using the lightest loads you can find. Winchester makes some Low-Noise, Low-Recoil target loads that are great. They're under an ounce of shot and loaded to relatively low velocities. If you reload, you can do the same thing for far less money. The only problem can be that they may not have enough "oomph" to cycle some autoloaders.
If you are using a single-shot 12ga, you can use "Li'l Skeeters" sub-gauge inserts, allowing you to shoot 20ga (or even better, 28ga) shells in a 12ga barrel. The recoil is quite manageable.
FWIW, a 20ga will often recoil just as much as a 12ga, since the 20ga will typically be of smaller scale and therefore weigh less. If you dig through the archives here, you'll find a lot of info and recommendations for younger shooters.