Budget is an important driving factor for any vacation -- balance it with your time to truly absorb the beauty of the places you will see! I chose Orvieto as my home base for a year living in Italy. It is a beautiful ancient city and well worth seeing.
If your personality likes the freedom that a car offers -- rent one, but the trains are both a mode of transportation and an opportunity to let your brain rest! Driving in Italy absolutely requires a SatNav system -- most roads don't have signage when you get south of Florence.
I personally love Lake Como -- it has several small villages that offer great views, restaurants and the water ferries let you sit back and enjoy the beautiful villas perched on the hills. If your first priority is to see the Dolomites, you may have to make a choice in order to give yourself the time to travel and to stop and enjoy the beauty.
Not sure if you are a "foodie" but you can schedule a truffle hunt excursion during your dates. I have one booked on 10/2 and am very excited for the experience. Your dates are also very good for scheduling a wine tour -- some of the best known Super Tuscans offer a morning tour and a lunch with their prestige cru vintages. For these activities a car would come in handy.
The beauty of Tuscany and Umbria deserves to be enjoyed without checking your watch every few minutes worried about missing your train or trying to check off every village and hamlet. Lucca, Siena, Pisa, Assisi, Orvieto -- all special and worthy of your time to see and experience. RS is right on track about getting off the main tourist drag and finding small trattorias and even a sandwich - have a sandwich picnic on the steps of a Duomo or in a nice park, like the locals!
Don't miss seeing at least a couple of the weekly markets. Como actually has a very good one on Saturdays --Everything from the produce stalls, cheeses, meats, clothing, linens, and jewelry, etc. Orvieto has a much smaller version on Thursday and Saturday mornings from 8:30 until around 12:30. There are specialty markets in many small towns that are fun, and sagres to experience a food theme for a taste of the region and its culture. Coming up in early October are truffle festivals!
Send me a PM if you are going to visit Orvieto -- I would enjoy meeting for a glass of wine and hearing about your trip -- and perhaps a drive into the countryside (I do have a car).
Enjoy your trip!
Catherine