I would probably do best with my food budget simply going to
the closest store with reliable fresh merchandise
that we like
and seeing what is the best price that day,
and getting the amount I know my family eats, and planning our meals around that --
using every bit of the food that I possibly can.Some people -- like my dad! -- have memorized the ever-changing prices -- of many of their nearby stores! with the help of their sales flyers -- so could plan their grocery list a bit more specifically ahead of time. Actually, most of us could somewhat -- like, summer squash is often inexpensive in late summer here, winter squash in midwinter, so we can plan a dish around that, though be open to changing that if something happened with the store's suppliers and prices were unusually high.
"The amount I know my family eats" is based on nutritional stuff, which differs for everybody. We feel best with a huge amount of vegetables, for example, and plenty of olive oil.
Speaking of olive oil, some ingredients from certain brands are more expensive, but can be the only reliably tasty ingredients. Constantly experimenting with other brands can be more expensive, to say nothing of unpleasant and even wasteful if the other brand is truly inedible (like some "unclean" stuff that made us ill, from a store I now avoid). I simply get a lot of our favorite brand when I see it on sale, especially for olive oil, vinegars, and spices.
There are very helpful, much more timeless cookbooks that help with the last "bit" of The Big Idea, using up every bit of food -- cookbooks like Save with Jamie, which I've mentioned already, that give advice on using your whole chicken in many tasty and easy ways. Jamie's book even gives great ideas on using up your vegetable scraps.
Of course it's only fresh food whose scraps are useable -- so food "on sale" that's icky is no bargain, though a bruise or two to trim away is perfectly fine....