All major car rental companies have locations on or near the Walt Disney World property, with pick-up and drop-off at your WDW resort hotel. I've had excellent service and cars from National at the WDW Dolphin, but I would not suggest limiting the choice to National and Alamo, despite their "official" status at WDW.
For example, Hertz has locations at around a dozen hotels in the general vicinity of Walt Disney World. (Some, but probably not all, of them all have shuttles.) Hertz also has a free-standing Disney-Kissimmee location on Hwy 192 just south of Disney's Animal Kingdom. It specializes in service to WDW resort guests:
Hertz - Disney World Kissimmee
7471 West Irlo Bronson Memorial Highway
Kissimmee, Florida 34747-1723
Phone: 407 396-2800
Location Type: Corporate
Hours of Operation: 0730-1700 7 Days
If you are loyal to a particular car rental company or you qualify for a good discount code through your employer or other affiliation, visit the website (or call the toll-free number) of that car rental company website.
Here are a few suggestions:
As the city, specify "Lake Buena Vista" or "Walt Disney World" (not Orlando) to bring up locations on or near WDW property.
Be sure to check the hours. Unlike busy airport locations, local car rental locations have limited hours.
The location information on the website might tell you how they handle pick-ups and drop-offs, but it would still be worth making a quick phone call to the location.
Although this thread is great idea, keep in mind that locations and hours will change over time.
It's worth trying different companies, different locations, and different legitimate discount codes to find a good price.
The location that's closest to your resort may not be the most convenient one if you have to wait to be picked up anyway.