Bodily Injury (BI) Liability insurance is for when you are at fault in an accident. It pays for the other party's bodily injuries or death for which you are responsible. This type of coverage pays for medical bills, loss of income and/or pain and suffering.
You will want to purchase at least your state minimum coverage for BI. If possible you will want to purchase coverage above that minimum so that insurance will cover a judgment about you if you are sued by the other party. Recommended coverage by then insurance industry is $100,000 per person and $300,000 per accident. This should be high enough so that your personal assets, such as your home, are not at risk. You can never buy too much insurance.
Property Damage (PD) liability insurance covers damage to another person's vehicle or property when you are at fault. Again each state has minimum requirements but it is recommended to get coverage above that amount so that your personal assets are not at risk. Between $50,000 up to $100,000 per accident is considered good coverage.
Uninsured motorist coverage is for bodily injuries sustained by the insured and members of the insureds household from an accident caused by a driver who does not have enough insurance or is uninsured. Experts in the insurance industry recommend buying at least $100,000 per person and $300,000 per accident.
Each state has its financial responsibility laws or minimum auto insurance requirements. It is always recommended to buy above that minimum and get the most auto insurance you can with your financial means.