We had a car and took Overlord because we didn't have time to do our homework -- it was a last minute add on to a trip to Paris and we had 5 days in Normandy. But I noticed that there seemed to be pretty good parking at the beaches and the American cemetery and it seems to me that someone who is willing to study up and plan their visit well could easily do it by car which of course gives you the freedom to add a village or stay longer at a museum or whatever. We were very happy with Overlord but no reason you could not do your own trip.
25 years ago my daughter was a student in Brussels and she and her mates did a Normandy WWII tour by car; one of her fellow students was a WWII buff and acted as tour guide and she said it was one of the best experiences of her life.
When I did this about 10 years ago, it would not have been necessary to get museum tickets in advance -- we visited the airborne museum and the museum at the American cemetery.