I think if we’re talking about “real dystopian collapse”, as in a major population reduction, there are going to be more leftover bullets than you could shoot in a dozen lifetimes. If you’re thinking about hunting small game, get something that shoots .22 LR and don’t waste your time with slings and arrows.

And with that being said, trapping small game is more efficient than hunting with any kind of weapon, so if you wanted to learn bushcraft for hunting for food after the end, that’s where I’d start.