We are arriving at 6 AM at the airport. Would you recommend the train or taxi to get into Rome? We will have to wait hours before checking into our air B&B
Taking the Leonardo Express from FCO to Termini is very easy. Also, the train station offers luggage storage. Since you're staying at an Airbnb, this would be really helpful.
Unless you’re staying in an out-of-the way place, then the Leonardo Express train is the way to go. You can always take a taxi from the Termini train station to your lodging, if it’s not within walking distance.
At the airport, once you’ve cleared immigration control and have your luggage, following the signs for train, you’ll pass red ticket vending machines on your right, and you can get Leonardo Express tickets there. We had some uniformed attendants at the machines to help us make the purchase - helpful early in the morning! The doors to get to the train platform are just past those machines.
I make these kinds of decisions based on funds available, but also based on my traveling companion(s). When I arrived in Rome with my frail sister, I took a taxi. I was personally dealing with all of our luggage (my backpack and her rolling carry-on, her extra checked roller bag and her personal item), and we were both tired. She walks slowly, and she uses a cane. An official taxi with a pre-set rate to central Rome was reasonable. On other trips, I have taken the train to Termini Station. If you are able-bodied with minimal luggage, take the train. It is fun to get off at Termini Station!
If you were arriving later and could go directly to the Air b&b, I would take a taxi.
But in your case, take the train to the station, store your luggage and explore
We were in Rome in January (3 people) and took a taxi and it was great.
My only caution is insist on an official, white-colored, licensed taxi. As we approached the stand at the airport an official-looking woman greeted us in English, confirmed that there were 3 of us with 3 big suitcases, told us we’d need a minivan and motioned to follow her. At first I thought she was going to pull the 3rd/4th taxi out of the line, which was a larger vehicle, but then she wanted us to walk away from the stand. So I repeated “official taxi” a few times while pointing at the stand and she suddenly vanished. I suspect she was taking us to her buddy who drives an unlicensed van and would charge some inflated price.
As it turned out, the luggage did fit into the back of the regular taxi that was in the front of the line. The driver took us right to our pensione for the flat €55 fare.
Good luck with the trip!