For much of the last 8 years as the economy crashed down I have been living of the stores I put away when times were good. They are pretty much all gone now but it literally saved my live and kept me off the dole the last several years of hard times.
The first thing you are going to need is to build a basic store of food for each person in your family.
Get airtight food storage containers. I get them second hand from several fast food restaurants from the store managers I know.
I also purchase airtight food storage bags from big box stores.
For each person store 300 pounds of rice or barley or wheat (that is six (6) 50 pound buckets)
150 pounds of beans or peas or lentils (three 50 pound buckets per person)
50 pounds of honey per person.
If you have this stored per person you will be able to provide a basic one years worth of rations per person.
Now you can expand your food storage stockpile to make it more interesting but this will keep you and your family alive in a disaster.