Quick question FCO to central Rome

Fxed rate is for a taxi with 4 people and luggage
No tip required

https://community.ricksteves.com/travel-forum/italy/taxi-or-private-transfer

Take the taxi. The fare is for up to 4 people and their luggage if you will be within the Aurelian walls

I've done both ways (train from FCO to Termini and a Taxi).

Personally I'd just do a taxi, you are likely tired when you arrive at FCO and it is nice to be dropped off at the hotel with no extra hassle. 55 Euro is pretty reasonable for a taxi in a major city.
The train definitely works, but you have to deal with Termini which is infested with pickpockets and then finding your way to the hotel.
I've learned over the years that if taxi's are reasonable in a city, then use them.

55€ is all inclusive for all 3 of you + luggage. Since your hotel is walking distance from Termini, the train is an option, but for 3 people the savings is only 13€. Save yourself the extra walk and hassle and have the taxi drop you in front of the hotel instead.

Be aware that taxi drivers prefer cash (primarily for tax dodging purposes***), and sometimes their POS machine "breaks down" or "does not get any wireless signal" (wink wink). So, before you board the taxi, make sure you either have cash, or make it clear that you can only pay by card.

*** The Italian tax laws permit small business owners, including taxi drivers, to pay a flat income tax of only 15% (or even only 5% in the first 5 years of activity) if their total annual revenue is less than 85,000€ per year. By getting paid in cash as much as possible (and not reporting that untraceable cash revenue), taxi drivers manage to stay under the 85,000€ revenue ceiling and qualify for the low flat tax rate. Paying them in cash will make them much happier than any tip you might want to leave (Don't leave tips to Italian taxi drivers! Ever! It's a mortal sin that not even the Jubilee can redeem)

Question - does that flat rate cab fare apply in the other direction - from a central Rome hotel to the airport?

Yes
The fixed rate is for either direction

And…if you are paying cash, be sure you are carrying small bills..fives, tens, twenties…. not fifties or hundreds.
You may not get the correct change back if you pay in large denomination bills if the driver is a little “shifty”.
Card is best.

Great!!! Thanks for the info.

Depending on where you're going in centro, there may be less expensive local train options--but as others have said, since you'll likely be tired and it wouldn't save THAT much money, a taxi is a fine option. :)

Terrific discussion! I am in the same boat and I was sure everyone was going to say take the train because it is faster. But after a long flight, the transaction cost of getting to the train finding the train getting off the train then finding your way to your hotel or apartments….That taxi ride is sounding very appealing for three people.

To get a taxi at FCO I assume it’s like any other airport there’s a taxi line? Returning to the airport, do you call a certain number for a taxi ( If you don’t live near a taxi stand. We are staying in an apartment). Thank you

Also look into the private drivers who will meet you inside the terminal with your name on a sign.
They are often less pricey than the regular airport taxis.

Rome Shuttle Limo is one company I've used a few times.

Careful. Our experience is the reverse. The private drive has always been more expensive than the fixed rate taxi.