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.

Good luck.

Ditto what Steve 1911A1 said. Only way to CYA.

from wiki

Overview of handgun licensing

The purchase of a handgun in New York State is limited to only those individuals who hold a valid Pistol License issued by a county or major city within New York State and present to the seller a purchase document, issued by the licensing authority, with the specific make, model, caliber and serial number of the handgun indicated on the document. The possession of a handgun in New York State is limited only to those individuals who hold a valid Pistol License and are in possession of a registered handgun (one that appears on the license, indicating the specific make, model, caliber and serial number of the handgun). The carry of a handgun in New York State is limited only to those individuals who hold a valid Pistol License, possess a registered handgun, and are carrying said handgun in compliance with the restrictions as they appear on the license and other applicable state and federal law.[6][7][10]

New York State pistol licenses are not issued to out-of-state or part-time residents.[10] New York does not honor licenses or permits from any other states, though some states will recognize New York licenses without a formal agreement.[11] There are no provisions for an out-of-state handgun owner (other than on- or off-duty law enforcement, on-duty military or non-resident business owners with a NYS Pistol License) to carry a handgun within New York State. A pistol license is required to physically examine a handgun for purchase at a gun store or gun show.

and thats JUST the state, nyc has even MORE hoops and god forbid you want to carry....