To complicate it more, do you even want fish or would crayfish or some other aquatic animal do a better job?
Some of it depends on what you like to eat, and whether your focus is more on using the fertilizer from the fish for growing plants vs. using the plants to filter the
water so you can grow tasty fish. If you want an equal balance - great fish plus great vegetables that becomes a little more tricky.
For getting the most fertilizer value, you can't beat goldfish. Known in the aquarium world as "messy fish" they'll put more nitrogen in the water than just about anything, and they're cheap to buy if you use plain old feeders. Or for
profit you can buy small koi and then
sell them in the spring when people want to stock their ponds. As the size goes up so does the price on Koi, phenomenally!
Other than that, it depends on your system. Trout like cool, running water - hard to do if the summers get hot where you are. Many fish give off hormones that limit their growth in overcrowded situations, and I've never gotten a clear
answer whether the plants in an aquaponics system would remove them or not. I know bluegill get stunted when they're too crowded.
If I were doing it, I may go with crayfish. There's a kind called marmorkreb that clones itself and doesn't eat its own young (unlike many other kinds of crayfish). You can
feed them plant waste, they tolerate a range of water temperatures and even some pollution if your system has kinks that need to be worked out. I had some for awhile and they're fascinating - the mother carries the eggs on her tail and the young when they hatch for awhile then they go off to hiding places and grow. Some crayfish go through a nymph phase but marmorkrebs start out as tiny crayfish. Without territorial males fighting, marmorkrebs are amazingly peaceful.