Make a list of what you're family uses each week, and how much. Knowing what you're going to need, how much, and how often, is the best way to anticipate what you'll need in an emergency. Starting off with items that will be most at stake in a food shortage crisis is a good idea. Items such at meat, cheese, butter and wheat products come to mind.
Start off by slowly building your supply. Bringing home items that are specifically meant for storage every time you visit the grocery store is a good way to build up your emergency shelves. If you have a garden or a greenhouse already, you can begin to can and dry your veggies and fruits.