green,
Unless you plan on visiting locations along the way that are not well served by trains or other public transit, taking the train would be a better option.
I assume you're aware that you'll need an International Driver's Permit for driving in Italy? IDP's are used in conjunction with your home D.L. so you'll have to take that too. You'll also have to be extremely careful to avoid the ZTL (limited traffic) zones which exist in all the places you'll be driving. Each pass through one of these areas will result in hefty fines, which you likely won't know about until several months after you return home. Florence is just about saturated with automated ZTL cameras so don't drive within the city.
A few points to note......
The rail station in Siena is at the bottom of the hill, so with "big luggage" you'll need to use a Taxi back & forth to the station. You could also travel by Bus from Florence to Siena, as the bus drops passengers right in the main part of town. The rail station in Orvieto is also below the city but there's a Funicular so it's easy to get up to the city.