I think other posters have already mentioned the alternative of getting the
Alamo/National shuttle to the MK Car Care Center. It is *free* from any WDW resort. A couple of things...
*Arrange the rental reservation ahead of time & watch those rates like a hawk! They do fluctuate quite a bit. Go to MouseSavers.Com's Rental Cars page - there will be lots of hints/tips/codes to help you pay less for your rental(yay!)
*You need to arrange for shuttle pick-up the day before your rental starts. Just talk to your resort's front desk, they should be able to help arrange this.
Taxis are fine, there are usually several waiting at a resort's check-in area, but that is some $ that could go for Mickey Bars...

. We've had car rentals that started during our WDW vacations after we came in from the airport, a couple of times & had no problems. Shuttle pick-up was quick & on-time, renting from the MK Car Care Center was fairly painless.
Something to be aware of...sometimes it is cheaper to rent for a longer period of time than you think you might need. For instance a "week"(5 days or longer) rental can actually be less than a three-day rental...odd, but true. This happened to us one year. A 9-day rental was far cheaper than a 7 day! Play around with any codes that you might be eligible for, change the rental duration...you might be surprised. Something else - if you rent from the MKCC, you won't be paying that nasty 'Airport Concession Recovery Fee'.
Have fun - you'll be at DisneyWooooooooooooorld

,
agnes!