If you're talking about the cheapest rental car insurance to cover the vehicle itself against loss or damage, the only insurance that is sold by the car rental companies that will cover that is the LDW (Loss Damage Waiver) or CDW (Collision Damage Waiver).
Read more about CDW and LDW Coverages
(ALI or SLI - additional and supplemental liability insurance will only cover other people, property and vehicles - not the rental car itself, the accident insurances that are sold are for medical coverage, not for the vehicle).
Read more about Liability Insurance
LDW and/or CDW is the most expensive type of car rental insurance coverage to purchase, and when you rent a car for a month, it can often double the price of the rental!
You may wish to check with your own personal automobile insurance policy adjustor to see if you already carry some loss/damage coverage for rental cars.
You can also check to see if the credit card that you plan to use offers LDW coverage on a rental car.
Make sure to be aware of the terms and conditions of either of these coverages, such as deductibles, vehicle restrictions and possible length of rental restrictions (especially for such a long rental) -- credit card rental car coverage generally only covers rentals of a certain length; make sure that you check to make sure it would be valid if you rent a car for a month.
Credit card coverage may be reimbursement type coverage; meaning that if you damage the rental car, the amount is charged to your credit card and you then have to submit a claim for reimbursement through the underwriter that covers the loss damage waiver coverage for the credit card company.
If you do not have or do not wish to use personal policy coverage or credit card coverage... your best bet is to check various companies and compare total costs of the rental plus rental car insurance coverage rates for the full term of your rental.
Some car rental companies may offer a partial damage waiver. I've seen this offered at National. It's an option called LDW 3000.
Basically, National waives up to the first $3,000 of loss or damage to the rental vehicle. The renter or authorized driver(s) pays for any loss or damage in excess of $3,000 up to the full value of the vehicle. This car rental insurance coverage averages around $12 per day when you rent a car for a month. (Their full LDW waives the renter's and authorized driver(s)responsibility for loss or damage to the rental vehicle up to the full value of the vehicle including administrative and loss of use fees. It averages around $23 a day when you rent a car for a month).
I haven't seen this partial damage waiver option with other companies yet, but it may be something that all car rental companies will begin to offer.
If you're looking at liability insurance coverage (if you do not own a car or have your own car insurance), as opposed to loss damage waiver coverage; most insurance companies do sell non-owner liability policies (if you wanted to purchase it yourself) ... also, this type of coverage (third party public liability and property damage) is usually included in the base rate when you rent a car for a month or even just a day -- up to the minimum limits required by state law. (check your preferred rental location for details.
Pages from this site, relating to this topic:
Car Rental Insurance Overview
Personal Protection Offers