This is what I did to find all the fish species:

1. find a fish (usually a magic fish) that sells well
2. breed it over and over to make lots of money
3. buy all the upgrades, ornaments and magic plants with one exception - do not buy the plant of fertility - this may seem odd as the extra offspring would be useful in the early stages of the game, but take it from me that it becomes a pain in the latter stages as you run out of space in the tanks.
4. I recommend keeping a pair of each of these magic fish: Magic fish of fertility, magic fish of growth, the golden guppy. Price your magic fish at $9999 and you can store them out of the way in your selling tank. They won't sell at that price!
5. Concentrate on finding all the species of a particular breed. e.g. Fruitfish. When you are breeding, don't have the greenfin spotanus (magic fish of fertility) in the tank - you only want to produce one of each species otherwise you'll run out of room.
6. Buy fish eggs, growth hormone and unknown chemical to help you find the missing fish from each species. When all 21 have been found, sell the fish and start again with a new species.

It takes a lot of juggling between the tanks and often you have to overprice certain fish to stop them selling, just so you have room to store them all!

Every once in a while, concentrate on breeding and selling your most expensive fish to raise more capital.