Best way to travel from Fiumicino Airport to Capri?

That probably would be faster when you factor in the the time to rent and drop a vehicle. And probably a lot cheaper. And much smarter when considering that you will be jet lagged and driving is not recommended. The car would add nothing to the journey.

I can't think of a single good reason to rent a car and drive the route from Rome to Naples - especially if you were thinking about doing that upon arrival from a long flight from North America. After you peel yourself off that flight, you are not going to be in any kind of condition to jump in a car and drive anywhere, never mind Italy. With convenient trains available, why would you want to do that?

Personally, I'd just take the trains all the way to Sorrento and catch the boat there.

"Best" is always a relative term but there is a shuttle bus from Fiumicino to close to Napoli Centrale/Garibaldi stations if you don't want to make the transfer to Termini. I've never used it but reviews aren't bad. It probably takes a little but longer but could be close enough to a wash depending on wait times for either trains or shuttle.

http://www.fiumicinoexpress.com/?lang=en

You could catch a cab to the port for the ferry from the Naples train station.

I wouldn't suggest driving all jet-lagged right off an international flight.

Personally, I'd just take the trains all the way to Sorrento and catch
the boat there.

The reason I personally wouldn't suggest this is because of the number of transfers it would involve:

Express train to Termini
Trenitalia "fast" train to Naples
Circumvesuviana commuter train to Sorrento
Transfer (bus or taxi) to the Sorrento port

If the shuttle bus works, you could do it with just one transfer: Naples train station to the Naples port.

Ferry schedule here:
http://www.positano.com/en/ferry-schedule?from=napoli&to=capri

Fair points. I like traveling by train - especially after being crammed into an airline seat overnight, I find a nice train ride more relaxing than a bus ride, but if it means you have fewer complicated tasks to perform, that's a plus (really, after flying from the US to Italy, most people are pretty wiped out both mentally and physically, and certainly in no shape to drive).

The "best" way to get anywhere depends on how you define "best". Cheapest? Fastest? Most scenic? Personally, I think the "best" way to get most places is by private helicopter...the choice of Presidents and Popes can't be too bad. It helps if someone else is paying.

Personally, I think the "best" way to get most places is by private
helicopter...the choice of Presidents and Popes can't be too bad. It
helps if someone else is paying.

LOL! I'm with you there, David!

BTW, I like trains too but the Circumvesuviana isn't exactly up to the standard of the Trenitalia "fast" trains (!!!) and could be a shock to the poor OP's system on (tired, jet-foggy) arrival day. I'm good with it for getting around cheaply but best if one is well rested and a little acclimated to Italy before taking that one on. Let's just say that the shuttle bus would definitely be more comfortable. :O)

There is the Campania Express train for Naples>Sorrento but it has so few daily runs that it's tough to make it an efficient choice for very many journeys.

NOT a rental car. One needs to be 100% alert. The laws and 'customs' on driving are different!

To the repeat the obvious

Renting a car for this trip is one horrible idea for many reasons.
Some stated above, others include where do you return the car? How do you get from car return to the ferry?
The biggest one though is Naples should be on most everyone's list of places to never drive in!!!
I would personally feel comfortable driving most anywhere in Italy but Naples is on my never drive closer than the airport list.

Train seems like the best option
Bus second
If money is no object a private driver would better those of course.