I assume you've already looked at specific tips for those plants, so skipping the obvious stuff. From my own experience as an apartment grower:
Go for a pot that's at least 10-12 inches deep. Personally, I'd recommend going for a felt/fiber based cloth pots, as these naturally drain very well, encourage the roots to spread out more evenly, and also helps keep the soil areated and prevent root rot. Regular pots can cause the roots to bundle up, inhibiting their growth and can also lead to root rot.
Don't use actual soil, as it may compact and hinder root growth. Use a high-quality potting mix instead. A mix designed specially for vegetables or one that's well-draining would be ideal.
Make sure your plants get plenty of sunlight (6-8 hrs) . A south-facing window is ideal. If natural light is limited, consider using grow lights. If you're using grow lights, 12-14 hours might be required.
Regularly check for pests like aphids. If detected, spray with a mix of water and a few drops of mild soap, or use an organic natural pesticide, like a neem-oil based spray (and don't go overboard).
The key to avoiding pests and fungal diseases is to ensure a good airflow between plants, try and maintain a distance of 1ft between the pots, if possible.
Without knowing your growing zone or how long you have before your region's frost date, it's a little tough to make certain recommendations. That said, I'm in favor of anyone experimenting and gardening so I say go for it!
Check what the germination period is on the seeds you are thinking of growing and add those days to the "days to maturity" listed. If that's past your average frost date you may have a tough time. Some spinaches are hardy enough to get stronger (and tastier) after non-killing frosts.
You should be good with the spinach and radishes, we're in 5b and are still within the window to get harvests on both of those. I haven't grown kohlrabi before so I can't speak to that specifically but I'd expect them to do pretty well for you. If you include onion or chives in one of the pots you could expect to get scallions as well.