I used to have a deck garden in Chicago about 6 years ago. You just need to be careful about draining fluids onto your neighbors. Normal flower pots weren't a problem, but larger pots and raised beds need to have irrigation or something to sit on so they don't leak sludge onto your neighbors deck if that's an issue for you. Otherwise, what you can grow is only limited to your climate and space available. I had a raised bed big enough to grow basil, parsley, cilantro, and spring onions. Then I had 2 very large pots, one with cherry tomatoes and one with mint. I had issues with rats and squirrels stealing stuff from time to time, so I generally kept the size of what I grew pretty small. Might be difficult to grow root veggies or large things like squash, but you never know until you try.

What direction does your deck face? I have a south-south west patio on my apartment and I grow tomatoes, assorted peppers (bell, banana, horn, jalapeño, habanero, ghost, Carolina reaper etc), blueberries, strawberries, raspberries etc. I was thinking of getting an apple and lemon tree next year. Basically if you aren’t facing east or north you should be good to go

I'm in an apartment with a north-facing balcony - I definitely wish I could grow more, but you'd be surprised how much you can do. I've successfully done carrots and potatoes in 5-gallon buckets, as well as pots of herbs.

This time of year I get sun until mid-morning and after mid-afternoon - it might be for the best actually that I'm shaded from the noon sun.

This year I've got snap peas growing up the railings, a couple of peppers, and a few tomatoes as well as the carrots, potatoes, and miscellaneous herbs. Everything's doing great right now but when it really starts getting hot in July I'll be watering at least daily. That's the biggest challenge with containers - they need a lot more watering because you just don't have the volume of soil to keep it damp for long.

I also have a shelf of salad greens under grow lights inside. I definitely recommend that, they grow really fast and taste great!

I've noticed snow peas tend to do very well in balcony conditions. If you don't get much sun, there are a lot of flowers that'd be much happier in mostly shade. Leafy greens are an extremely good option, they're quick to grow and they don't need as much light.

I've got a bunch of cherry tomato ripening right now. Herbs grow great. Carrots, onions... deck gardens definitely work!

tomatoes are pretty fickle, so you may have an easier time with something else, but generally it is doable. if possible, look for varietals bred for container-growing, as they'll often be smaller plants. I've never grown peas or beans myself but I bet green beans and various peppers would be good choices.

of course, familiarize yourself with your environment. determine your plant hardiness zone: https://www.fs.usda.gov/wildflowers/Native_Plant_Materials/Native_Gardening/hardinesszones.shtml and growing seasons. as others said, the direction your deck faces is important, but since you're in an apartment, you may actually have an advantage of being able to utilize reflected light from the building facing you as well. (I used to have a north-facing deck and the brick wall opposite me was a major source of light for my plants, which would sometimes reach toward it)

A friend of mine would grow sweet potatoes and the vines would drape over the edge to get.more sun. I bet it looked really cool from the street. I think she didn't really do it for the yams but hey, free yams!

I've grown mint on my deck before. Mojito mint is my personal favorite. Also great for a drink haha.