We lived in Augsburg, Germany for four years and have driven in my car many times in Europe. It is a great way to see the countryside, places like Normandy, Tuscany, Switzerland, Bavaria and more.
Having a car is a liability if you plan to stay in major cities like Paris, Munich, Rome and more. The European highways are excellent in Germany, France, Italy and Switzerland. Roads are not as good in the Balkans and Greece. I don't recommend that you drive a car through the Balkans or in Greece. First, it is too far to drive and Second the roads are not as good and you will waste a lot of time getting to Greece. You can still make it to Greece by air, cheap flights are available. Getting to the islands is recommended after a few days in Athens. Actually, a cruise is not a bad idea, but there are ferries that go to Mykonos, Santorini, Rhodes, and more.
Driving in Europe is similar to North America, but then again not. Yes, except in the UK and Ireland, you are on the right. Drivers in Europe tend to be more aggressive, especially in Germany. The autobahns are like our interstate highways, but speeds are faster and you need to stay in the right lane unless passing.
France and Italy have the equivalent of autobahns, but the tolls are quite expensive, especially in Italy. If not on an autobahn, the back roads can range from poor to good. Many back roads follow the old trails that were not engineered like modern roads.
If you go to places like Normandy, driving a car is great, but plan your route and have a navigation system or GPS. Road signs may not be as good as they should be. Staying in large cities, plan on turning in the car. If you go to Italy places like Rome, Florence and Venice are not auto friendly, consider getting rid of the car and take the train to and from those cities.
Another thing, fuel for your car will cost you an arm and a leg in Germany, something like three or four times what it costs in the USA.