RER is the cheapest way to get to Paris and it’s fastest if there’s any road traffic. The Air France bust is mores expensive, slightly faster if there’s no traffic and considerably slower during rush hour. Whether or not to get the 10 pack, Paris Visite or some other option depends on which days (one card is Monday through Sunday — not good if your stay is Thursday through Wednesday as you’d need 2), where your hotel is located and how many zones you plan to travel in.

Renting a mini-van will probably be the cheapest option for Paris to Rome. I would also look for cheap flights and investigate the overnight train. 6 people in a mini-van for a long trip does not sound like a good time to me and it might not be all that much cheaper by the time you figure fuel, parking, extra local transportation costs in order to stay somewhere that has parking, tolls, drop charges, taxes, insurance and extra charge for a 2nd country on the rental contract.

In Rome, you’ll probably mostly be walking. The subway is cheap. You can buy an all day pass (also good on buses, I think) for about twice the price of a single subway ride. We bought the all day pass, but usually wasted it as we took the subway out to the farthest place we were visiting that day and generally walked back to the hotel — only took the subway back to the hotel when it was raining.