The limited tank space has caused all of us a certain amount of agonizing over which fish to keep and which ones to sell!
There is no simple answer as to which fish to keep. There are so many possible fish in the game that it would take a LOT more tanks than you have to hold them all. You can use all of your tanks for breeding, but any adults you have in your selling tank will be for sale, so you have to be careful when you hit the "Sell Fish" button that there aren't any fish you want to keep in there.
The good news is that there are many, many ways to breed each of the possible fish, including all of the Magic Fish. Taking a systematic approach to your breeding cuts down the stress of having to sell off a bunch of fish because your tanks are full. One approach (once you have fully researched Fish Environment) is to keep a fish that interests you (e.g. a Spotanus), and breed it with each of the other fish in the tank. Once the babies are born, sell all of the parents
except the Spotanus and breed it with the new fish once they grow up. If you keep doing that, you'll soon have some fish you've never seen before.
Many of us have kept track of our breeding results as a way of managing the large number of fish, using everything from simple spreadsheets to impressive databases. It's the only way I found to manage all of those fish! Of course, you can always download one of the breeding references in our Fish Tycoon Guide section.