If you own your own vehicle then you will need to obtain auto insurance on it. Since you are a minor your parents would need to sign on the policy with you.
If you do not have your own car then to be properly insured to use your parent's vehicle you will likely need to be added to their policy. Teens are not normally automatically covered by insurance without parents informing their insurer of their child's licensing status. Some insurance companies will cover a teen when they have a permit or provisional license and wait until the child is fully licensed before requiring them to be added to the policy. Other insurance providers will require the child to be added to the policy as soon as they start the licensing process, meaning when they have a permit or other type of license during the graduated licensing process.
As the New Jersey Department of Business and Insurance (DOBI), the insurance regulator for the state, notes you should notify your parents' insurer when you are ready to obtain your driving permit.
Any change in their insurance cost will either apply when you receive a permit or license, depending on the insurance company's rating plan. As the NJ DOBI notes, failure to disclose all of the drivers in a household to your insurer can be construed as a form of Insurance fraud, which is subject to policy cancellation, civil fine, or penalty under the New Jersey Insurance Fraud Prevention Act.
The DOBI also states that most insurers offer discounts for multiple cars, so it will most likely cost less for a young driver to be added to their parents' policy than to purchase their own. However, any driver with a car titled and registered in their name can purchase insurance in NJ.
So if you live at home with your parents then they should advise their insurance carrier of your licensing status and their insurance carrier will tell them if you need to be added to the policy at this time with only your provisional license or if it can wait until you have a full license. This way your parent's will know what is needed of them to have you properly insured while operating a vehicle in New Jersey.