when considering "subsistence hunting" my first pick is the 10/22 loaded with subsonics.

in non-sporting survival senario when only hunting small game (and when the cost/weight of ammo is weighed against the dressed weight of the game is included), i don't see the need for a shotgun (SG), because birds can be taken on the ground with a 22lr. (yes, this is non-sporting and illegal in most cases. i'm talking emergency survival only).

OTOH, if the consideration includes sporting uses, then both 10/22 and SG are useful tools.

for a simple safe inexpensive SG, i like the Stoeger side-by-side double-barrel Coach Gun in 12ga, which sell here for around $300

and while a 12ga sounds too powerful for kids, light loads are readily available that don't kick hard, yet allow the kids to grow into using more powerful loads as the need arises.