The cheapest car insurance, period, will likely carry the minimum coverage required in your state. In most states, this is liability insurance only, which covers property damage and medical bills for others due to accidents you cause. Some states also require uninsured and underinsured motorist coverage, which pay for your injuries or damage if an at-fault driver doesn’t have enough insurance.
Third-party claims occur with less frequency in no-fault car insurance states, where you first look to your own insurance company to recover, regardless of who is actually at fault for an accident or injury. Generally, no-fault states have mandatory minimum insurance requirements, meaning that every driver carries a statutorily dictated minimum amount of insurance. If, after you’ve made the appropriate claims to your own insurance company, your claim meets your state's monetary threshold or "serious injury" threshold for stepping outside of no-fault, you may be able to initiate a third-party claim.
If you have paid off your car, comprehensive coverage is optional. It may be a good idea to find out the Kelley Blue Book value of your vehicle. Would you be able to pay that amount to repair or replace your vehicle if it were stolen or damaged in an accident? If you can't afford to pay much out of pocket, then buying optional coverages, like comprehensive coverage and collision coverage, may be a smart investment.