We did a private car from NRT to TDR, but only because the limousine bus wasn't running when we arrived. Unfortunately, I can't recommend because the driver didn't speak English and the communication was frustrating. I regret not just taking a taxi. There were many lined up while we were looking for our car service.
Another regret is not asking more questions beforehand rather than relying on the e-mailed instructions. If you do decide on a car service, I think the easiest would be to have meet and greet service.
That said, we've taken the limousine bus before from TDR and it's very comfortable. They help you with your luggage and store it underneath the bus.