Its important to think in multiple layers: For example carrots and salad on the ground, tomatoes on top and way above beans.
One thing I would always recommend: potatoes - one of the most robust crops, that almost always work out.
For a balcony, the fun and the created atmosphere should play a role alongside the yield. You won't match your need for calories anyway...
Can you elaborate or link to a picture, please? What you're saying does sound interesting and I would love to have tomatoes too, besides beets and carrot. But I'm not sure how I would do it.
To give you an idea of what I have at my disposal- 3 balconies (except east), all small, 2ft by 20ft. All have iron railings which could come handy for the right type of veggie I guess. ..
