New York State (and City) firearms laws follow a logic all their own, and have absolutely no relationship to any other rationality known to mankind.
Further, the laws of each and every New York State county is different from those of any other.
If you wish to possess a gun in New York State, you need to consult New York State laws, not us firearms owners. New York State, like all of the states of the US, maintains a website on which all of its laws are published and indexed. If you do not feel competent to consult that on your own, I strongly suggest seeking the specific advice of an attorney licensed to practice in New York State.
You may need a permit to merely purchase a firearm, depending upon in which county your receiving FFL licensee operates. Or, you may need no permit to purchase, but you will need a permit merely to possess subsequent to the purchase.