To buy a shotgun in NJ I had to get three notarized letters from people (non family) declaring how long they knew me and stating that I wasn't a danger to anyone to their knowledge. And fill out a lengthy form. And wait a couple of weeks to get approved. And wait another week for an appointment to get a permit to own a firearm. And get fingerprinted.
Other than that though it was really fast and easy.
That’s what I need for a premises permit for a handgun in Nassau County. Long gun, as long as it it not among those proscribed is same day service.