I like to push the scarcity. So yeah, you have to buy, barter or gather food yourself. Increasing the food attribute of the Ark makes this easier as food per bullet increases.
I've always thought that the campaign starts after that shortage becomes apparent. There used to be a large central store, but that is down to a few weeks or a months supply now, hoarded by a combination of the people around the Elder, the bosses or a few lucky fixers. The Ark at the lowest food stage has no way of producing food besides the odd bits stalkers bring home and decide to share.
I think you should do what feels interesting for your Ark, and what fits the people you have controlling the food. Maybe a boss has a labour-for-food routine where you do your day's chore and then get your allotment under guard. Maybe you go to the fixer's grub auction.