Interesting request. Glad you are thinking about it before you get started because you will get a lot of different input from the people who work for the state. The reason is that they are used to dealing with the masses and you are asking for an exception.
Start with calling the DMV and ask for the special titles (or maybe foreign titles) unit. When you get connected ask for them to send you an application. There is a .pdf attachment posted in Club Cobra that shows the documents that they will send you.
From then, just follow their instructions and talk to some folks who have gone through it. You may get different input depending on which specialty station they took it to and you need to decide how you want to register it (collector or straight inspection [you need a pre '74 block to get emission exemption]).
In a nutshell:
1.) Fill out the application and send it to the foreign titles unit in Trenton, register it as a 'reconstruct.'
2.) Get the car inspected at one of the three specialty stations in NJ, Morristown, Asbury Park or Atlantic City area. Note: you cannot drive the car until you have it registered so you need to trailer it to a station.
3.) Get the title (once the station has inspected and passed the car
and sent in the paperwork to Trenton)
4.) Take the title and proof of insurance to your local DMV for plates (if you want collector status bring along the policy that shows collector status somewhere), fill out the application for collector status at this time.
5.) Drive the car to the local DMV inspection station. If you get regular registration, the car needs to go through a regular inspection like any other car. If you got collector registration, they will just check the mileage (3,000 per year).
Good luck. Might be a pain but once you get behind the wheel and get it on the road, it is worth it.
Joe K