We had a huge garden at our last home (we moved last fall and I am SO looking forward to starting an even bigger garden this year). My boys always had a garden, so I just kept growing what I had been, and these were their favorites (I think you could do most in a container):
Tomatoes - especially the cherry ones. They can pick them and eat them right in the garden. If you buy plants designed for patios they'll do great in containers.
Green beans and sugar snap peas - you can do pole beans on trellises and run your peas up fences as well. Not sure how peas would work in a pot, but I would think that pole beans might do ok.
Broccolli - we eat a lot of broccolli in our house :) Last year I found plants that produced purple broccoli flowers! They were super fun.
I love the idea of a pizza garden!
Any kind of garden you can get done with little ones teaches them so much about life, patience, food, and it's a great thing to do together!
Good luck!
Jessica