You can use the gun you've already got. Or borrow.
That is, if you have any kind of a shotgun whatsoever (field or single-barrel break open, etc.), preferably in 12ga. (but a 20ga will work for openers), then you could let your son shoot that shotgun for a season or so to get him started. Even a side-by-side.
Any shotgun that will put a decent pattern downrange will work for a season to learn beginner trap rules, ropes, and practices.
Then if he sticks with it (which is always subject to the whims of a teenager) by then you'll have something specific in mind and you will have some solid experience in the sport. Then you can make a good, solid informed purchase.
You will hear all kinds of arguments about fitting the shotgun to the shooter, best starter gun, yada-yada-yada.
And.............Most of what you hear will be more or less true.
Nevertheless, just about any pump, semi-auto, break-open, double, O/O shotgun will break clays.
When he goes for the regionals or nationals, then that's the time to think Krieghoff, Perazzi, or even a Browning Citori, whatever. And if he gives up the sport, you get your shotgun back.
FWIW,