Campino is a little far out from Rome city so best to take a shuttle bus to either Roma Termini Central sation (8 euro single / 14 euro return)or Anagnina sation (1.20 euro)
Going to keep this quite simple as first time in Italy & do not want to stress ourselves out with lot sof travelling. Will spend first few nights in Rome & then on to Amalfi Coast where we'll base ourselves somewhere & see Capri, Pompei etc as day trips.