It’s important to distinguish between whether your are making an aquaponics system that has decorative fish or fish that you plan on eating. Systems with the goal of being decorative can use fish that are typically found in pet stores for aquariums, such as goldfish, guppies, or betta fish.
Image from: www.petinfoclub.com
Or if you are looking for a larger fish breed, koi are a great option and are used widely around the world for decorative aquaponics.
If you want to eat the fish that are in your aquaponics system, some recommended breeds are African tilapia, barramundi, carp, catfish, and perch. Make sure you know the water temperature requirements of the fish that you want to purchase, and adjust your system accordingly.
Image from: denstormerpresents.com
It is also always important to make sure the tank or container for your fish is large enough for the species that you choose--fish need space to swim around! A happy fish equals a happy aquaponics system.
*Title photo from: http://stratfordmanagers.com/fish-where-the-fishes-are/