According to the New Jersey Motor Vehicle Commission within 60 days of becoming a NJ resident (or before the expiration of your out of state license), you need to purchase a NJ examination permit so that you can get a New Jersey driver's license.

You will need to purchase a permit for each class of vehicle you will be operating. After doing so you need to visit a driver test center (DTC) to take a vision test, knowledge test and possibly a road test. After you pass the required tests, the DTC will tell you how to obtain a permanent license. When you receive the full NJ license you will have to surrender your Pennsylvania license.

New Jersey state law requires that any registered car be covered by auto insurance by the state minimum liability insurance limits of 15/30/5. You should be able to obtain this insurance as you are getting your NJ license. Since you are going to be a resident of NJ and garage the vehicle in New Jersey it should be registered and insured there.

You can find out if you need to acquire New Jersey insurance before or after registering your vehicle in NJ by contacting the MVC. Once you are ready to obtain New Jersey insurance for your vehicle you can get free car insurance quote here.