I did respond to your earlier request for help, but, since you didn't ask me for additional help, I assumed that you wanted to experiment some on your own.
The best thing to do is to continue to spend your money on researching Fish Environment until you've reached level 3. Once you have that, you will be able to breed any fish without worrying about them losing health and dying. At a level 1 Fish Environment, only common fish will remain completely healthy, although some hybrids will survive to adulthood, at which point you can sell them.
Once you have level 3 of Fish Environment, one method to increase the number of species you discover is to breed one fish with every other fish type that you have and keep the new fish that you find. Then breed those offspring with the original fish. You should soon find fish you've never seen before. Once you've done that for a few generations, you can repeat the process with a different set of fishies.

If you want spoiler-type solutions, check out the Spoilers threads in the Fish Tycoon Guide section of the forums.