A separate farming station
Whether connected as a separate cylinder from the living spaces or as a separate station nearby, you would want to build a place to do the farming. You would not really want to do it in the same place as the humans are living for various reasons.
Plants will not have the same temperature, gravity, atmosphere, and daylight requirements as the people. In particular, if you develop vegetable crops that can grow year round (like cabbages from the arctic circle that are accustomed to 24 hour days in the growing season), you will then want to keep these plants in full sun at optimal temperature (likely around 30 C) permanently. 30 C, and full 24-hour sunlight might not be the best conditions for people.
Since you would presumably develop low-gravity plant variants, your primary concern would be shaping a habitat so that it faced the sun (or got reflected sunlight) 24/7 to maximize growth per space. Space is your primary constraint; fertilizer and water are cheap compared to space stations. It is worth your effort to make optimal growing conditions to get 6 harvests per year to save space.
These conditions would probably not be great for animals, so the spacer would likely be a vegetarian. You would lean hard on beans and other pulses to meet protein requirements. Hope you like tofu!
Building vertically and trying aeroponics would probably not be useful. Since you are making your own station, you can design its geometry. Your geometry should involve the most area with applied sunlight possible, and that area should have gravity applied tangential to it, as on Earth. Plants will need some sort of gravity for their pressure based internal mechanics to work. Then you can grow Earth plants, slightly modified for space on this area. Aeroponics is great in theory, but there does not exist highly productive aeroponic breeds of corn, soybeans, lentils, potatoes, whatever else you want to eat. There do exist highly productive varieties of those plants for use in soil, so you should go with that.
So, in conclusion, develop a specialized farming station to grow your food at optimal conditions. This will give you the most food per area/volume while you are in space.