I have flown into both Rome airports. The second one, Ciampino, is south of the city and does not serve any trans-Atlantic destinations, although it does serve many routes to other European countries.
The best way in and out of the city from FCO is by train.
One thing I do not like at FCO is their new terminal for high terrorist risk destinations, namely the US and Israel. The terminal is austere, and for a time did not even have any food service, although it has limited service now. It is also not so secure, as you have to get to it by bus from the regular terminal and the bus stop to get there is outside of security, when means they concentrate those potential targets all in one place which has no security at all.