Rome-Florence-Venice would be a bit too much for a week trip IMO. In Rome alone you could easily spend several days to visit the top spots. For the Colloseum + Forum Romanum you would already need a full day.
I agree with other replies here: For Rome and Florence (and also Venice) I would take the train but for Siena and Montalcino and other smaller Tuscan cities (Pitigliano would be on my must-see list) I would recommend using a car. This also will allow you to make some trips and enjoy the amazing scenery.
My trip would be something like:
Hire a car at FCO, drive to Montalcino off-highway via Pitigliano. Spend 3 nights in Montalcino with a few winery visits, a visit to the Sant Antimo Abby (preferably experience a Vesper or other mass in Gregorian), a trip to Pienza (Pecorino-city) and generally enjoy the great wines during lunch, dinner and in between. Il Giglio is a great place to stay & a great place to drink some of the most amazing wines from their cellar.
Then I would travel to Siena (the nr. 1 favourite in my family) and stay for a few nights. A daytrip (by train) to Florence is easy from there. The Duomo is amazing, there are excellent restaurants and outside July/August craze it is a relatively relaxed medieval city. Personally I find the main square (Il Campo) one of the most beautiful places in the world, I would at least have a cappuccino, lunch and a dinner there. If you fancy a nice drive I would recommend a trip to Radda in Chianti or Arezzo on the local roads. You will see so many familiar names of towns, if you know an Italian wine or two...
Then I would go back to Rome, hand back the car, and spend the remainder of the days enjoying the thousands of things to see there.
After celebrating our 20th Tuscan-summer-holiday this year I might be a bit biased but I think we could spend a full year exploring this amazing part of Italy.