Air Rifles and slingshots
An air rifle is a great tool for hunting small game or pests. It’s silent and you can re-fire used BB’s, as long as they aren’t too messed up. BB’s are also pretty cheap, you can acquire a lifetimes worth for less than $100.
Slingshots are another great hunting tool, as you can find ammo anyplace around you, even under your feet. That’s because slingshots can use rocks and pebbles as ammo. Free ammo and silent, the only downfall is that it’s easier to aim a BB rifle than it is a slingshot. It’d also be worth noting that it would be easier to repair a slingshot than a compressed air powered rifle.
If you want to eat some rabbits, squirrels or birds in a post TEOTWAWKI survival world, then you should really consider one or both of these economic choices!