Um...there's no waitIng period for NY as far as I know.
You get your paperwork to apply , fill it out, get pictures taken for the permit,in some counties take a firearms safety course, and send it in. The issuing office ( generally either the county sheriff or local police ) do a thorough background check, and then send a request to the bureau of mental health in Albany. They send back the info, and the sheriff puts his opinion on it and sends it to the judge for approval / denial. Most counties estimate 6 months or more from start to approval.
Once you're approved it goes like this ( depending on the county ) . You go the the LGS, find a gun you want, pay the man and he gives you a bill of sale . You then take the bill of sale to the county clerks office, and put the pistol on your permit. They give you a purchase coupon, which goes back to the dealer . You go back, give him the coupon, and walk with the gun. Thats the middle ground.
My county, I can buy 3 purchase coupons from the clerks office. I walk into the LGS, find a gun I want, pay and walk out. I then have 10 days to go to the clerks office and put the gun on my permit.
This is handguns only BTW.
In a couple of more restrictive counties, there is more **** to deal with. They're generally the counties with a larger city where the liberals hold the vote. My buddy has a restriction on his permit, basically given to all who apply and get approved, of on premises, hunting and range travel only. This is in the Syracuse area. In the binghamton area I bought my 460, the guy said that you make the purchase, then send all info to the judge and he has to approve it, then you get your coupon.
None of this applies in the 5 counties that make up NYC .