Car Rental Insurance – Which is necessary h to buy if not US citizen?

I am not a US citizen., but will be renting a car for 2 weeks from Payless. Will need advice as to what is the necessary car insurance to buy if :-

1. The accident is not due to my fault ?
2. If it is due to my fault.

I have travel insurance which covers me for medical insurance due to accident but not the other party , and also has a deductible for car rental.