Transfer

Depends on your hotel location. The airport website has a transportation section with the available options
https://www.adr.it/trasporti-cia

A taxi cab from official stand.

Taxi from the stand is 30-40e into the center of the city fixed price with 10e for further destinations. There are buses that run to the main train station Rome Termini and one that makes a metro connection. The train is not really convenient requiring a bus connection as well.

A taxi is the most direct but metro/bus will be cheaper and may work well depending on where you're staying. With luggage I would probably choose a taxi just for the convenience. Taxi is also fixed rate up to four so with more people it makes even more sense.

Enjoy Rome,
=Tod