We just returned from Great Exuma and we rented right from Thompson's at the airport, which we had reserved in advance. I did not purchase the insurance as my credit card has coverage for rental cars but you may want to contact your personal auto insurance agent to get his thoughts.
Make sure you get a decent car from Thompson's. Ours smelled like smoke and the battery died on the second day leaving us stranded for a couple hours on the way back from Cocoplum beach. They replaced the car, temporarily with another while ours got fixed. This whole ordeal required me to drive to their shop at the airport a couple extra times and was a major inconvenience in the middle of our vacation, but all in all, they seem okay. If nothing else, it is conveniently located.