Some grocery store chains tend to carry better deals than others. If you can set aside some time to list the food products you typically buy, and compare the costs among local grocery stores, you'll get a general idea about which will give you the best deal. But don't stress over individual items. It's probably too difficult and time consuming to split your grocery trip up into multiple stops for particular items.
As we've already discussed, as long as you know what to look for and avoid in a supermarket, you don't have to shop at pricey organic markets to eat healthy foods. A smart shopper is a frugal shopper, and this doesn't just apply to food. When the family is on a budget, you should research any significant purchase ahead of time.