I would really reconsider renting a car. You will spend more time, energy, and money dealing with the logistics of "the car" than you will enjoying Italy.
I have been to Venice then onto Rome 7 times and each time I have gone a different route (usually through Tuscany, using buses) and used different means of transportation.
The best way I've found to go straight to Rome from Venice, is to take an overnight train from Venice, that way you save having to pay for a hotel room that night.
There were sometimes "strikes" that halted transportation for a few hours, but they are well announced ahead of time, and easy to plan around.
There was a taxi strike the morning we needed to go to the airport, but our desk clerk drove us for the same amount a taxi would have cost. The desk clerk LOVED taxi strikes!
No cars are allowed in Venice proper (the islands); thus, if you drive to Venice, you have to park in certain areas. The only place on the islands themselves that you can park is at Piazzale Roma, which is at the end of the causeway coming from the mainland.
See http://www.urbislimen.net/eng/index.html for an online parking reservation site associated with the City of Venice. Through this site, you will find that parking at Piazzale Roma is now 21 euro/day and parking in Mestre (on the mainland) is 10 euro/day.
Of course, once you are in Piazzale Roma, you can immediately start walking in Venice. If you are in Mestre, you have to catch a train or bus over the causeway into Venice - this will add to the cost and time. I would guess that for one person, the train fare both ways would not be nearly up to the 11 euro difference...but the more people you have, the less sense it makes to park in Mestre, since train/bus tickets are per person, and the parking rate in Piazzale Roma is per car. Well, I am saying that it doesn't make sense to kill yourself trying to save a couple of euro...see http://www.trenitalia.com/en/index.html for the train schedules and fares from "Venezia Mestre" (hopefully the mainland parking is close to the station), and "Venezia Santa Lucia" (on the islands, where you want to go).
Also see http://www.comune.venezia.it/flex/cm/pages/ServeBLOB.php/L/EN/IDPagina/119 which is the City's official website that lists all sorts of parking alternatives...
We booked this on the web. Staff were helpful and spoke good English. We left the keys with the car, car was protected and at Euros 20 for 12 hours in the centre of Venice we considered this good value. Would definitely recommend. It is only a couple of minutes away from the vaporetto stop for the Grand Canal
The majority of visitors to Venice all arrive by car. Quiet a problem since the "streets" of Venice are all waterways. Hence after you have crossed the bridge from the Italian mainland in Mestre it is time to leave your car - on offer are a number of parking garages and parking areas to the right (after crossing the bridge) where you can leave your car. Piazza Roma is within walking distance, and from here one can explore Venice on foot, by water taxi or gondola.
We have driven to Venice for a couple of our visits, and found that it is extremely easy to just park at Marco Polo airport. From there, you can either take a water taxi directly to your hotel or take the water bus to stops throughout Venice.
If you are arriving in Venice by car in the summer it would be advisable to make parking reservations ahead. You can make the reservations on-line. We park at the Piazzale Roma Garage and find it very easy to find and the garage has good access to the Vaporetti station.
As you enter Venice over the bridge the parking garage, a many storied building is directly to your right. The long line on the right can be avoided by reserving your parking ahead. The entrance for reserved parking is the short line on the left.
Parking car in Venice might be a huge problem, so many visitors arriving here in cars and very limited space. One can wait more then one hour for free parking place in Park S. Andrea, as I did, and finaly it costs me 16,52 euros for 7 hours. The alternative is the Garage San Marco which charge you 24 euros per day.
The best solution is to park your car in Mestre, for free if possible, and get to Venice by the public transportation.