A small garden is not going to provide you any meaningful quantity of basic nutrition: carbs, fat, or protein. So, rather than focusing your efforts on staple crops like corn and root crops, I suggest planting crops that will enhance the flavor and vitamin content of the staple food you are going to have to get elsewhere anyway. So plant herbs, tomatoes, peppers, onions, garlic, greens etc.
I would like to start a garden but I have a small area to use. What things can I grow that would take up the least space and provide the most calories/nutrition?
There is a book, too.There used to be an old show on TV called "Square Foot Gardening" and it specialized in just this sort of thing.. Showed you how you could basically plant anything in a square foot setting.. So people living in apartments in manhattan could have their own gardens... somethings you could only grow 1 to a foot but others you could grow alot more.
I'm planning on buying or having all the rice and wholewheat flour to make bread that I'll ever need, so my vegetable garden will be more along the lines of spinach, collards, tomatoes, onions, garlic, peppers, broccoli, etc..