Pretty hard to beat a Ruger 10/22: inexpensive, fun and customizable...Not as accurate as some others out of the box, however, more than adequate for everyday plinking. Note: Dick's Sporting Goods had them for $199 last week.
My first rifle was a Marlin 60 and I regret selling it some 20 odd years ago. My sons first rifle was also a Marlin 60, I tracked an OLD one down at a pawn shop. They still make them, but they're harder to find and like the 10/22, you want an older one. There is too much plastic on the newer ones. That being said, I have 2 10/22s in the safe and recommend them over the Marlin just because of the options available. You can change them up as much as you like and even make some VERY accurate shooters, I've seen guys dump thousands into them. Modifying them becomes a hobby of it's own.
You can most likely scratch the 96/22 off the list. They are out of production for a while.
The lever action 22 are over the price point except the Henrey basic model with the plastic barrel band and front sight.
I would look into the used market but time before christmas is short.
At 14 i had a single shot steven model 15 with iron sights, Put more ammo thru it than about any rifle i own. If i had a 10-22 i would have put more ammo thru it as i would have not had to cock it each time,
At 16 i bought a 10-22 and it rocked my world with the crappy 4 power scope.
If he can shoot all kinds of ammo then the auto. If like my dad said "here is 5 shells bring home 4 tree rats' then maybe a single shot is better.
I think one person said the CZ lineup. These I have seen shoot as well as a quality winchester target rifle at the matches, better than tricked out 10-22's.
Get a Savage bolt with an Accu-Trigger. The bolt action is a great teaching rifle and it will save you money several ways. 1) Bolts are much cheaper to shoot because it takes more time to squeeze off a magazine. 2) Great trigger out of the box, no need to upgrade. 3) The Savage is much cheaper to shoot than a 10/22 because there is little to change or upgrade, unlike everything you point at on 10/22 can be upgraded for some extra $$.
That said, I have both and enjoy them for different reasons.