Having gone down the gun for kid road 6 times (that' how many kids we have) I would find something mild recoil and either I wanted as well or I could unload should they loose interest. I wouldn't go break the bank to get started, if the shooting will also include hunting that's something to consider. Of my 6 I have twin girls who are now 18, one likes to hunt and the other has zero desire. She likes to shoot, but as they age into teen years the time with friends become greater and less time with us.
I said all that to say this, a 6mm (anything) is a good shooting option accurate, mild recoil - checks many boxes. There are plenty of mid range options on optics - remember this is a kid and most do not take care of things like we do. But it's your wallet, like buying them a new car at 16, but some of the biggest issues kids have these days in the "real" world is they can't afford what daddy bought them and those days are coming. I spoil mine too, but i have to remind my married ones in there later 20's you are gonna go broke trying to keep up with the jones's!
I'd do somethings over again, but then again wait till the grandchildren come - pawpaw will have some cool ****!