PLPD insurance is about as basic as you can get. It stands for Public Liability Public Damage, and is intended to satisfy the requirements of the state, but nothing more. In essence, PLPD covers damage that you cause to someone or their property, and all remaining costs must be paid out of pocket, including repairs to your own vehicle, or any peripheral costs such as towing or the use of a rental car.
By contrast, no-fault insurance covers you and the passengers in your vehicle, along with any damage it sustains. Under no-fault coverage, insurance companies pay out for their own insured, and then negotiate the settlements according to who is finally deemed to have caused the accident. No-fault coverage also makes it difficult to impossible to file a counter suit against the other driver or their insurance company.
Lastly, full coverage insurance, as the name implies, covers a wide range of damages, including property and bodily injury to you and your passengers and the property or bodily injury caused by you to other people in an accident. This coverage will cost quite a bit more than PLPD coverage, but also gives you coverage for a lot more scenarios. And remember, PLPD may seem to be less expensive, but one serious accident could create financial difficulties that your budget is unable to cope with.