Here's what I think I'd grow:
Potatoes - Incredibly easy to grow. Produces a ton of food. Can be grown in trash cans on otherwise unusable land. Very versatile and useful in so many cuisines. If I had to place my bets on one staple crop, it's potatoes.
Green beans (Blue Lake variety or similar) - Also very easy to grow. You trellis them and they don't take up a lot of ground space. Incredibly bountiful crop--you'll have trash bags full from 50 sq ft of beans. Puts nutrients back in the soil--very good crop to rotate.
Kale - Nutritious, versatile crop. Easy to grow.
Tomatoes - Nutritious and so easy to grow. Can be grown vertically in raised pots for more space efficiency.
Tomatillos - Tasty, good for sauces. These grow as voraciously as the green beans.
Pumpkins, squashes, etc. - These are wandering vines so you can plant them in good soil on the edge of unusable land and let them grow out over the areas that you couldn't plant in.
Various lettuces - Not easy to grow--they're susceptible to pests and they bolt as soon as the weather gets too warm--but they grow fast and if your family likes salad, you'll eat a lot of them.