Apply for your permit. List the Luger ser# (back in the 70s when I lived in NY, they wanted maker, Ser# barrel length & caliber). Follow the process, and be patient. The gun will have to be picked up from an FFL dealer in NY, AFTER you get your permit listing it.
Contact the dealer you plan to use, they will help you out and walk you through the process (and likely charge a fee). Pay them and don't whine, there is no other legal option (unless you can find another dealer who charges less).
Getting a NY permit listing the gun is registration. You are covered there.
Also, be aware that permits issued outside of New York City are not valid in NYC. Even though you can have a valid permit for the rest of the state, if you take your gun into NYC, you are breaking the law as it currently exists.
All else being equal (and it almost never is) bigger bullets tend to work better.