Hey fellow apartment grower! I'm not sure what your growing space is like, but on my second floor southwest facing balcony, I've had the best success with arugula and other leafy greens, kale, chives, peas, beans, jalapenos, and basically all the herbs. Larger plants like cucumbers and tomatoes can get big FAST (even when pruning) so be sure to opt for a dwarf variety or be prepared to set up a trellising system so you can manage their growth a bit more easily. But it can be done, and it's really satisfying.
I've learned the hard way that with container
gardening, you have to really keep an eye on the moisture and temperature levels. Last year I was not very diligent with my watering schedule and my corn, tomatoes and cukes ended up with a bad case of verticullum wilt at the end of the season that spread around the garden. Just be aware that plants need appropriate spacing for air flow and to
water in the morning so your plants can let the excess moisture evaporate through the day. This year I'll be building some wicking/self-watering containers and using ollas to build a little more resiliency when it comes to the usual issue of fluctuating between too much and too little moisture. With that in mind, I think you could actually grow just about anything (except maybe giant pumpkins) so long as you give each plant what it needs to succeed (which will be very dependent on the environment).
P.s. If you're working with a small space, you can apply the Square foot gardening approach to container growing for a rough idea of what kind of spacing you can get away with per 1ft(ish) container. Here's a handy lil pdf:
http://plantandplate.com/p-downloads/PlantandPlate-SFG-spacing.pdf
P.P.S. There's a balcony gardening webinar tomorrow if you wanna sign up!
https://www.miinikaan.com/resources