Don't feel stupid....many people make this error!! You're not the first, nor will you be the last.
As far as the car goes....it depends on what you need and what the cost is. I've rented a car in Sanford before, and kept it for the duration. But....that's because I was going elsewhere after my WDW stay. A lot of people rent and then the car just sits at the resort, until it's time to head back to the airport. Others rent one way....return it to the rental company once they get to the resort. But...the issue is which rental company to use. Alamo/National have two on-site offices. One is at the Dolphin Resort, by Epcot/DHS. The other is the Car Care Center, close to the MK. The CCC will give you a ride back to your resort, but you have to let then know ahead of time. They will also come pick you up if you want to rent to get back to the airport. At the Dolphin, you drop the car off and then get yourself to wherever it is you want to be.
There are other rental companies in the DTD area. Some have shuttles, some don't.