This is what I did for my kid.
Depending upon your skill level and time available, you may or may not want to do the same.
I bought a used T/C Black Diamond, less than 100 bucks. Cut about 3 1/2 inches of the barrel off and recrowned it, cut about 2 inches of the stock off and replaced the pad. Before I put the pad back on, I took an old sock and put about 6 oz of lead shot in it. The gun, while a tad heavy, balances exactly in the wrist. So, there is very little weight to support in the front, which is the problem most kids have. I then put a good 3x9 power bushnell scope on it.
I was initially concerned about how short the barrel would be and burning all the powder, until I saw some of the other short barrel models out there. Anyhow, I load it with 75 grains of 777 under a 300 grain Hornady XTP. Shoots 2 inch groups at 100 yards all day long. Already killed two deer with it. Handles very nicely, all my friends want it to still hunt with because it points very naturally and has a very sweet balance.

R
Hank