We have not rented a car in many years for our trips to WDW. Disney provides excellent transportation within WDW. Buses to the theme parks start service about an hour before the park opening. Early buses are provided for the numerous breakfasts all around the World. For the Magic Kingdom the buses start before 6:30am daily and 7:00am for the rest of WDW.
Even people who prefer to drive will tell you not to drive to the Magic Kingdom. Only Disney buses are allowed near the MK entrance. All other traffic must go to the TTC. From there you will either walk or tram to either the boat or monorail to the MK.
At park closings the buses will be crowded. Disney does provice extra serivce during all peak periods. My advice is not to rush out of any park at closing. Last June we watched Wishes and then sat on a bench across from the castle. We watched the throngs pour down Main Street to the exits. After 15-20 minutes we walked slowly out and the bus area was peaceful and quiet. Personally I cannot imagine it any easier trying to drive out with hundreds of other cars at park closings. Take your time and enjoy your visit. Disney will take you anyplace you want to go. If you have any plans to eat at the resorts simply plan on the nearest theme park for that part of the day. This will make it much easier to get to the resort to eat. Never try to get directly from one resort to another as there simply is no direct bus service. All service is from resort to theme park, theme park to resort, and theme park to theme park.
Taxis are available at all WDW resorts. They are normally waiting for fares but if one is not available the Cast Member working outside will get one for you right away.
Have a great trip!