@JEFFROSS: There exists a Three Caliber GunSet for around $400 By the Time You get it Home - Everything but a Scope! One Action, so you only have to learn how to shoot basically One Gun. Interchangeable Barrels.
It is called the "Trifecta" it comes in a nice fitted case, and has a nice array of Calibers for the various models of the Gun. It is From ROSSI, not a First Line Gun Manufacturer, but Perfectly adequate for Your Family Use. It would be Perfect for training Your Boys that "Each Shot Must Count". It is easy to see that is "Open, thus Safe". I am surprised that all the EggSpurts that have posted have not told you of this solution to your needs. It will Work as a .22, AND as a Long-Range Hunting Rifle, AND as a Shotgun.
It is a Break-Action Single Shot. To change Calibers, you detach the .22 barrel, and attach the 12 Gauge Barrel. Or the .243, or .223 Barrel. They also have .44Mag Barrels.and More!
Big Ugly Guy
Wow, you are rude. We were waiting for an "EggSpurt" like you to suggest a $400 gun.
If you shop around for used guns, you can get a .22 rifle, a 12-guage shotgun, and a deer rifle for around $400. If the guy is going to spend $400 he can have all three.
I did a search on Texas Gun Trader, and here is what I found. There are also several Mosin Nagants and Mausers for less than $200.
.22 riflle -- $100
12-guage shotgun -- $100
.243 rifle with scope -- $260