My favorite beating around and plinking guns are my old faithful Smith K-22 revolver, and my Marlin 1894 in .44 mag. I'm loving the lever so much, I'm wanting another in .357.
We have a couple CZ .22s; a Luxe and a Scout, both awesome accurate guns. If he is smaller, you could get a full size and then a scout stock to go with it so he can grow into it.
I'm a .22 nut, and have quite a few nice .22 handguns. My favorite goes with me almost every day-a 1949 Smith & Wesson k-22, the precursor to the model 17. I would go with an old model 17 if you like a 6 inch or a model 18 if you want a 4 inch for more frequent carry. Both very accurate...
I have no idea how many deer I have shot over the last 40 years. All but 1 was double lunged and never had to shoot twice (except once when I took 2 deer). I try for zero meat wasted, and the rib cage is an easy to see target.