Taking homemade concrete planter designs from Instructables, basic fish keeping and hydroponic gardening techniques, and putting it all together adds up to a highly adaptable aquaponic system you can use indoors with the use of LED grow lights, on your balcony, or on your rooftop. The use of concrete if done correctly, will prevent leeching of harmful substances you might get with the many plastics found in aquaponic setups.
Also, using concrete allows you to create forms that will fit any space.

In the concept illustrations, everything from small proof-of-concept systems, to larger, full scale rooftop production models are included. Although you could use pretty much any kind of fish, tilapia, minnows, and freshwater shrimp are eaten here in Thailand and at least tilapia and freshwater shrimp are very easy to keep. Even if you don't plan on eating them, investigating their integration into your project could in the future provide added value. Until then, they are interesting to watch, and produce lots of useful waste to be used by your growing plants.
If you are really into DIYbio, consider using zebra fish (danio rerio), considered a model organism for genetic research.