I want to set aside the NYC vs. NY State thing for the moment. I’ll cross that bridge when I get to it and find a legal solution for ownership, storage etc.
You need to deal with the legal solution first and foremost:
First, you will never get a handgun permit where you reside in NYC.
Second, you will need a handgun permit in order to legally purchase a handgun.
Third, handgun permits are county specific in that you can only get a handgun permit (outside of NYC) upon the approval of the county sheriff and county court judge in the county where you reside as a full-time resident.
FYI -- the way this works outside of NYC is that you must first obtain a handgun permit before you are legally allowed to even touch a pistol or revolver at a gun shop. To obtain a permit you must submit a lengthy application, fingerprints, photo, and four recommendations from non-family members who reside in the county where you reside, to the county sheriff in the county where you reside. After a two month to two year wait -- depending upon the county -- and assuming you pass the background check, a handgun permit will/shall be issued, but again, depending upon the county and the sheriff's view of the 2nd Amendment, the permit will either be full carry or limited to home, business, range, and/or hunting. Next, you take the permit to the gun shop and pick out your handgun and put down a deposit. The gun shop then gives you a coupon with the make, model, caliber, and serial number of the handgun, which you must then bring to the county sheriff, for processing, including another background check, and then to the county court judge for approval, which can take another two weeks to six months or more. You will then be issued a new permit with the handgun listed on the back, which you then bring to gun shop to pick up your handgun after passing the national background check. In total, you will need to pass three redundant background checks -- one when you apply for the handgun permit, one when you submit the purchase coupon from the gun shop to the sheriff and county judge for approval, and one when you pick the handgun up from the gun shop.