First and foremost, there is no ONE right food budget for all families, There are different food needs, different tastes, and different food beliefs. Decide what things you value most: nutritious food? Food you can trace easily to it's source? Convenience? Price?
Next, consider buying things in bulk - items that your family uses all the time and that you know you get through. Amazon Subscribe & Save program is a excellent resource, and often sells things for far less than the grocery stores. They also have great warehouse deals, always worth checking out!
One of the biggest things you can do is plan a menu, make a corresponding list of needed ingredients, AND THEN STICK TO THAT LIST IN THE GROCERY STORE! By only buying what you need, you don't spend needless money on impulse purchases.