Transportation from Airport to downtown Rome

By “best” do you mean easiest, or cheapest, or fastest or most comfortable?

Taxis have a fixed rate which most private drivers also charge. There is also is a train from FCO to Termini Station, the Leonardo Express.

If you have lots of luggage or difficult mobility, take a taxi or shuttle to downtown. The Leonardo express is a train that shuttles back and forth from Termini (the main railroad station) to FCO (Fiumicino the airport). The LE fee is 14 E/per person.

Cheapest, plenty comfortable but not fastest is an airport shuttle bus.
As with the Express train, they only go to main stations and some other central locations. We've used the buses and been fine with them but If your hotel isn't walking distance from drop-off points, you'll need to catch a taxi or take public transit onward. One-way tickets run as low as 5 or 6€.

http://www.adr.it/en/web/aeroporti-di-roma-en-/pax-fco-bus

Since you asked for the "best" way, here's my take. Use a private car service. After a long flight, some jet lag, not being familiar with the area, there is nothing better than having your private driver meet you inside the terminal and whisk you to your hotel. No fending off the "independent cabbies", waiting in the regular taxi line, or just having a "lost" feeling. It is not the cheapest way, but it is definitely the best. We can not say enough good things about Rome Cabs. It is a private car service (not a cab company) but only cost a little more than a regular taxi. We always use them and have always been very pleased. Go to romecabs.com and see what you think. We send an email detailing our needs and they answer us with a quote within 24 hours. You do have to pay cash (Euros) and the end of the journey but not in advance.

I normally use the Leonardo Express from FCO to Roma Termini, and then a Taxi to my hotel (assuming it's not within walking distance). Fare on the L.E. is €14 PP and travel time is about 32 minutes. If there are several people travelling, it may be cheaper to take a Taxi as they have a flat rate of €48.

Some important points to mention if you decide to use the train.....

• there are two different trains serving the airport, so be sure to board the correct one!
• you MUST validate your ticket prior to boarding the train, or risk hefty fines which will be collected on the spot!
• you may also end up on a Freccia train to Termini, and the fare for those is slightly higher at €19 PP.

I took a SIT bus from Fiumicino to the Termini last month for 6 Euros. I was staying on Cavour, near the Termini, so it was about a 3- minute walk from where they dropped me off. It departed about midnight. Coming back to the airport from the Termini I took the TAM bus from the Termini. It was also 6 Euros, one-way. It runs 24 hours. Both rides were just fine.