Ditto the 10/22, however if your budget permits, start with a single-shot bolt action and pick up the 10/22 when he's a little older.
Nix the .22 handgun for the kid, he's too young. (Or any other cannon somebody might jokingly suggest.)
Especially if inexperienced with the rifle.
Take it one step at a time as he gains experience and continues to exhibit maturity and safe handling.
(Now if Dad wants a .22 pistol to enhance his own target-plinking pleasure -- that's a different matter.)
But teach the kid responsibly on the rifle first.
My daughters can handle the Mark II and enjoy it. I seriously think that an 11 year old boy, with proper supervision of course, can handle one and it makes a great companion to a .22 rifle.
If someone wanted to argue that a revolver would be better, I'd not argue that, but I put guns in my kids' hands as soon as I could do so safely, and 11 is certainly old enough.