Old post, but hey, might benefit someone out there. If you're moving to NYS, it REALLY depends on which county you'll be moving to as to how likely you can get a pistol permit, and to what degree of carry they'll let you have. If you're moving here and you don't ALREADY have a NYS permit (even if you don't own any pistols) it's in your interest to get one anyway, as you still need one in many places to purchase pistol-caliber ammo in the state (even if it's not FOR a pistol). Even a premises or sporting permit is better than nothing (and is, of course, required for POSSESSION of pistols). In general, you need a pistol permit in NYS first, then you can register them with your county pistol clerk, once they're on your permit, you can then carry them to whatever level of carry you're allowed on that permit.
The safest thing to do would be to transfer any currently-owned firearms from an FFL near you to an FFL near where you'll be living in NYS (some gun clubs or really nice shop owners will do this for free or a nominal fee), but generally you only have to do that if you're a NYS resident and purchasing weapons out-of-state. If you're in a non-NYC county and you only have long guns with the appropriate mag sizes and nothing that qualifies as an assault weapon under the SAFE Act, you should be able to bring them in w/o issue if you already own them (you don't have to register these outside of NYC). If you're moving to NYC, you need both long gun permits of the appropriate type AND they need to be registered (same for pistols, which is a separate license). If you own 4 or more guns of any kind in NYC, you also have to show them proof that you have adequate storage (e.g. a safe).
In any case, definitely ask the pistol clerk in whatever county's sheriff's office you're moving to; some counties are more restrictive than others, and they can provide info on exactly what they need you to do based on where you're moving to.
