If you all want to fly TATL together, it really limits your choices and increases travel time, unless it is to a major airport (FCO or MXP). TATLs US-VCE are limited (DL only?) so such a plan would most likely involve a transit in the U.S. and another in Europe (does increase chances of a misconnect). Same with flying back from NAP.
Italian trains can be cheap, if you buy the tickets in advance (booking window is either 60 or 90 days, I forget). You will be limited to a specific train and missing or changing it would involve buying a walk-up ticket (expensive).