What is a good base to see this area either via car or/and train or other?
Acquitaine is big. Bordeaux or Sarlat are two famous towns in that region.
A combination of train and car may be needed. You should do research in the guide book to see where you want to go.
Thank you. Do you like any particular guide book?
I would try the book Lonely Planet France or Rick Steves France
and this official site was put together by the region
http://www.tourisme-aquitaine.fr/en/destinations/dordogne-valley/