I cant answer all of your airport questions, but from FCO to Rome we have done 3 ways of getting downtown Rome.
Rented a car - not the easiest as you have to watch for ZTL's
Took the Leonardo Express from FCO to Termini - then cabbed it to our apartment. Also you can connect with any metro line at Termini.
Hired a private transfer
The easiest and most inexpensive was the Leonardo Express €14/person and 30 minutes later you are at Termini
The private hire was €50 and was nice comfortable ride. It was about the cost of a taxi cab but a lot more plush.
The rental car we drove through Rome and not on the bypass strada towards Venice and was able to avoid all the ZTL's. (google maps doesnt care about ZTL's)
By train
Venice - Stazione di Venezia Santa Lucia is located along side the Grand Canal. Depending on where you want to go in Venice you can purchase tickets for a vaporetto or walk (depending on how much luggage you have) or splurge on a water taxi.
Florence - Firenze Santa Maria Novella is located a short, flat easy 10 minute walk from the Duomo complex.
Milan - Stazione di Milano Centrale - when we arrive in Milan we just head downstairs and grab the yellow line Metro to the Duomo stop and emerge in the Piazza.
Hope this helps.