NY is one of the worst states for handguns. It is one of the only states in the entire nation where it is a crime just to have a handgun in your own home without a specific license from New York.
Not a license to carry, a license just to own the gun!
If you move to New York and have a handgun in your home without a license you are guilty of a felony if uncovered.
The license process can also be relatively archaic. You need to cite references, and the references often need to reside in the same county! They have to be willing to help you get the privilege of owning a handgun in your home.
These references often cannot be relatives.
For example a quick search to give you an example turned up this for Ontario County:
http://www.co.ontario.ny.us/coclerk/PistolPermits.html
References:
Four character references are needed to sign the two applications and complete a reference sheet. The references must be residents of Ontario County and must be acquaintances of yours for at least five years. Character references may not be relatives of the applicant. References cannot be related to each other (ex. Husband and wife). If you are unable to meet the five-year requirement for your references, list the references anyway and specify the number of years you have been acquainted. Then you will also need to get 4 additional references from where you previously lived.
This means you would need 8 character references, some of whom should have known you for at least 5 years, 4 references from that county, and 4 from your previous state, none of them relatives, that would all say good things about you and recommend that you be allowed to own a handgun.
You then are expected to wait about a year for the application to be processed, and it would be illegal to possess a handgun until it is processed, and then only if you are granted the license:
Processing time for the pistol permit is approximately 8 months to 1 year after submitting the application to the Clerk's Office.