I suggest Tours, at least to pick up a car. If you're planning on staying a few days, I think Amboise would be a good base, centrally located to see all the chateaus, easy to get in and out of (downtown Tours is not especially easy to navigate), yet big enough to have plenty of choices of restaurants, etc. The Saint-Pierre-des-Corps train station is the one you want, on the outskirts of Tours. I love this part of the Loire Valley. If you're looking for a weekly rental, at least check out
http://www.slowtrav.com/cl/detail.asp?l=1619, my favorite rental of all time. It's out in the countryside between Amboise and Montrichard, but an easy drive to wherever you want to go. It is often available for less than a week, especially off season.