Do you see the big fluffy purple fish on the poster in the Fish Store? What is it called? Also, How does one get any fish with "Great Sail" fins?

If you're talking about the one at the bottom of the poster, it doesn't exist in the game as pictured. There is a red version of that one in Fish Tycoon.

There are only a few combinations that produce the Great-Sail fin, and you'll need at least one second-generation fish (such as Speckled or Razorback) to get it. If you go to the Spoilers thread in the Fish Tycoon Guide section, you'll see several resources that will let you look up fish combinations.