Honestly, most people should just store more of what they normally eat. If you just increase the amount of the normal, everyday foods you consume, they'll stay fresh, won't be wasted if the end of the world doesn't happen this month, and will actually taste good. Familiar, comforting food is important in a crisis, especially with kids. Plus, you'll be far ahead of the panicked hordes as they rush to the markets for basics to live more than a few days.
If you add more canned and non-refrigerated foods for the time you expect to need them, you'd be pretty well set. Buy a few extra cans/portions each time you go to the market, until you're a month or so ahead. It's a start.
Don't forget to also store lots of water. Probably more important, in the short-term, than food. Another issue is how portable you need this stuff to be. If you're leaving home, then specialty foods (light/packable) become desireable.
For longer term storage of grains and such, most people use 5-gal. buckets.