based on my experience taxy drivers in FCO very rarely accept credit cards.....and the same applies to any taxy in italy.....some do...but don't count on it!....there's a train connection (express and not ) to the main train station in rome (Termini) and from there loads of buses to get around the city.....and go to your hotel too i guess.
Rome is the most beautiful city i have ever seen. enjoy it!!
tmr