I would have also suggested going to Orvieto first, so it's great to see that you've decided to do that. You may not need a car for the first few days, depending on where you plan on touring in that area. Spend a day or two exploring Orvieto while you get over jet lag.
In addition to the IDP, be sure to do some research on ZTL (limited traffic) areas, as those exist in many Italian towns. Hefty fines for each pass through one of the restricted areas! Also, parking in Siena can be difficult at times.
The rail station in Siena is at the bottom of the hill, so you'll need to take a Taxi from the town to connect with the train. If you wanted to take a Bus back to Rome, the Bus station is in Piazza Gramsci in the centre of Siena, which is a bit easier. Trains on that route often seem to connect to a Freccia in Florence.
You may already be aware of this, but when you first arrive and take the train into Rome, be sure to validate your ticket prior to boarding the train or you'll risk hefty fines which will be collected on the spot! Also note there are two trains serving the airport, the Leonardo Express and the FL-1. Be sure to board the correct train! Validating locally purchased tickets applies to Metro, Bus and other forms of transit as well.