Do you want to be legal?
Legally in some states (NJ is one of them) if you are building a car that is not as original than you will have to get the car titled as a new car. You would have to pass a safety inspection (which I think most cars will fail one since most are just poorly thrown together or at least the ones I have looked at) and meet certain requirements. You would be issued a special vehicle title of some sort.
If you are in CA you can go to Boyd Cottingtons website where he tells you how to legally register your cars. BTW, you do not have to meet all the new car standards-- again read what is on Boyd's website. If you are caught in CA with an illegally registered car you will have pay some bucks to get out of jail.
Many people just get a title (many ways this can be done) for their year car and use that to register their street rod. This is not legal, but no one really checks in most states. Though I suspect as the states realize the revenue they are missing out on they may start to change how they enforce this. CA has already realized this so the other states are soon to follow (see Boyd's website). It is really not to hard to enforce since any car with historic tags shows the car was not registered a new title and then you just have to look a the engine an wheels, not too many Fords came with a 454 or a 350.
I would start by calling your states DMV title office and ask questions without giving your real name. The NJ office was surprisingly helpful. The process of legally registering your car may be much cheaper in the end over getting caught.
Also keep in mind if your car is not legally registered your insurance company might not have to pay off. Check your fine print. If the insurance companies figure this one out you have problems.