Debit Cards for your spending cash from ATM's, but your should also carry at least one Credit Card, we only used our Credit Card once on our last trip and that was to buy a set of Tea Cups and have them shipped.
Also don't bother with a Discover Card as they're not accepted.
We have rented a car from Dan Dooley with our debit card. We will leave next week for 3 weeks. We prepaid and had to take out full insurance, but we would do that anyway. The last time we beat the heck out of a rim and got chips in our windshield. The only thing we will have to pay is for the gas, and we can use our debit for that also. We just paid off all credit cards a couple of years ago and we don't even own one now! Also, there was no deposit held! I think you are OK as long as you have the VISA or MC logo on your card.