Ok first things first, here's a list of the fish you can buy without doing any breeding, just need to buy them with coins:
- Nice Fish
- Mean Fish
- Brave Fish
- Shy Fish
- Smart Fish
- Creative Fish
Those get pretty boring though, so you can either use pearls to buy more fish - or you can breed between two fish to get new kinds too. Here's the list of all the ones you can breed: Gamesdreams.com/showthread.php?5151-Fish-with-Attitude-Breeding-Guide-List-of-All-Fishes
My favorites are evil fish and ghost fish but I have loads of other iPhone games to play so I haven't been concentrating much on breeding too many fish.
When I do I will come back and update like on which ones I think are worth breeding. Some of them look pretty lame though. One of my friends has a "nerdy fish" lol.
Also just found this on YouTube. Nice video explaining how to breed fish. It's current from May 2013 though - so might need a little updating, but it gives you a good idea of how many options are out there - too many for me to type that's for sure!!!