OK...I have never had a problem with car rental, but my sister frequently does (she is handicapped so doesn't drive but has credit card- her DH is the driver, til recently <25, but has no credit card!), so here is what I've learned thru my experiences and theirs.
1. RENTER must have a credit card in their name. Although debit cards can be used to pay for the rental at the END of the rental period, a credit card must be used when you pick up the car.
2. Insurance is optional if you have FULL insurance (comprehensive and collision) on your own vehicle. Call your insurance agent to check this; you may have a rider that says they will cover rentals. The Dollar agent once told me that anyone who has a car loan for a car will have adequate insurance to cover rentals (I guess banks are very picky about insurance on the vehicles that they technically own!). They also said that if you say you have insurance, they usually trust that you are telling the truth. I've never been asked for proof of insurance, but carry a copy of my policy with me when I travel, JUST IN CASE!!! Also, check into gold/platinum credit cards, as most include automatic rental car insurance but remember that for the insurance to be valid, THAT is the card that you must use for renting the vehicle.
3. Drivers under 25 will pay an additional fee, MAY be required to carry rental company's insurance (although the legality of requiring company's insurance is questionable).
4. Additional drivers usually pay an additional fee of about $3-$5/day. HOWEVER, check out some things. My DH's employment at MSU gave him certain travel benefits, one of which is a contractual agreement with National. For business OR personal travel, using the MSU recap code, both rental insurance and additional drivers are free- and the contracted rental prices are generally very good (usually we can get an intermediate car for the price of an economy).
5. Budget accepts Sears credit cards! I don't think that Budget usually has the best rates, BUT if you don't have a major credit card and don't have time to get one before leaving, rent from Budget and use a Sears card. Need a Sears card? They usually will approve your application and give you your account number when you apply for the card at any Sears store.
FYI- my sister rents the cars with her credit card, then puts DH on as an additional driver so he can do the driving. It seems messed up to me- they'll rent a vehicle to an UNLICENSED person, as long as they have a credit card!
Hope this info helps--I'd hate for you to get to the rental car counter and have an "unfortunate" experience!