Relax. BIG breaths. Repeat after me: It WILL be OK, it will be ok . . .
imgoingtodisney, like others have said, if you are going to be only doing Disney, the bus transportation is really all you'll need. We NEVER have a car, but we stay with only Disney while we are there.
The buses run every 20 to 25 minutes. They are pretty reliable.
The transportation to the water parks may take a bit longer, 20 to 30 minutes.
If there are 3 of you, Mears may be a bit cheaper than a towncar, but not as convenient. You may have several stops on the way in and out. A towncar will get you there directly.
Really, don't worry about micro-managing your vacation. Remember to HAVE FUN!!!