I've been growing vegetables on my balcony for years now. The most important thing for me is to make sure the container is large enough. I grow from seed; there are many varieties of veggies that are specific for container growing, and I have grown a few of them. But I certainly don't limit myself to those varieties.
I must have tomatoes every year, usually trying one new-to-me variety along with one tried-and-true favorite each year. In addition, I'll grow peppers and herbs (must have basil 'cause I'm addicted to pesto). And each year I try a "new" veggie - cauliflower, eggplant, scallions, spinach, swiss chard,, etc., etc. I've even grown cantaloupe, raspberries and figs up here!
Check out some the food I've grown over the years ...

Veggies

PV

also meant to say - my balcony gets sun against the railing from about 11 a.m. to 3 p.m.

Mishell, good looking starts up there! And pvick, I visited your photo site. All I can say is, Wow!" I am inspired to try harder.