OH Grasshopper!!! There are thousands of street rods, replicas, kit cars, home builts, reproductions on the streets of America. Each state has their won requirements. Some are relatively easy and some are a pain in the arse and some have specific categories for such cars. Check your states dmv site for information on what is required. Local street rodder clubs would be a good resource. Mostly what is required is a certificate of origin of the body/chassis and receipts for the major components such as engine and transaxle. Some states required an inspection by the state police of the car and documents and other states just want the sales tax collected for all the parts before they give you plates and a vin number.
In Massachusetts a state police inspection of the finished car (must be painted) is required and there are differences what inspection station you go to. I had to make three trips before they issued a vin number. each time i went i fixed the issue from the previous inspection and they found another item to nick me on.
I had no problems with insurance. I had the car appraised and did stated value. Each state is a little different with this.