I have yet to try growing broccoli, but broccoli raab (rapini is another name) is one of my absolute favorites. It can be cut-and-come-again which in my opinion makes it a far better choice if you have only a small garden. (I'm curious to try growing sprouting broccoli, too.)
Swiss chard is another great green to grow. The "Bright Lites" version is so pretty, and it, too, is cut-and-come-again. 3 square feet of that (27 plants) ended up being far more than we needed last year! I gave away lots of it.
I am going to dispute the comment on beans. Bush beans may be small/easy to grow in containers, but there is a problem with them. They are programmed to come ripe all at the same time. If you are canning or freezing, that's great, but if you want a steady harvest of fresh beans you'll need to sow a few seeds every week or so and watch it carefully. I have small garden (backyard of a townhouse, all raised garden beds) and I like the pole beans. Yes, you have to figure out how to trellis them (and a little 4-ft cage is NOT enough! more like 6-8 ft) but pole beans--at least the ones I've grown--bear continuously once they get going. You can pick plenty to eat and still get a few bins full to do canning or freezing. At the end of the season they get away from me and I just leave the rest go and harvest the last ones as dried beans.
Beet greens are absolutely delicious. So are radish greens. I'm always turned off by the radish greens I see in supermarkets, but the fresh-grown ones are really good. Radish greens and wedged radishes, sauteed in a pan with a little garlic, olive oil, and cracked red pepper, is REALLY good. The flavor mellows.
I have grown amaranth once (for seed as well as leaf) and I'm still trying to figure out how to use it. My understanding is that when the leaves get large they can contain large amounts of oxalic acid and I'm not sure how serious that is...and I don't know where the dividing line is. But, it's an absolutely fantastic plant...look it up on Wikipedia. Grows very well under poor conditions. Mine did NOT like to be transplanted, even though I was very careful. If you pick a big variety be prepared to stake them if necessary. My non-transplanted plant reached 11 feet tall. (The others only got to maybe 5'.)
I grew up on a farm, but that was long ago. I've been seriously gardening for myself for two years now. Most everything has been from heirloom, non-GMO seed (rareseeds.com, hint hint...and no I'm not an employee!) and I suck at starting things indoors so I just stick them in the dirt and they grow. They may be a little later than if you start them inside, but they do just fine. I have yet to plan for my third year but I think I will focus more on the things I use the most of and that are the most expensive at the store, for the price...and still grow a couple of fun things. Have to have that!
If I had to give you one piece of advice, it would be this: Do not shirk on your initial setup. Keep it small if you have to. And always think about how you are going to get water to your plants when doing the initial layout.