The public transport system in Europe especially within each country is generally very good. However it will need very good planning and often sacrifice on some of the places to visit. It could also get expensive unless you are eligible for discount and/or plan well in advance. Except in the large cities, I have felt that depending on public transport results to lot of wasted time. Also travelling from one country to another could get horribly time consuming unless you are going only to the popular destinations.
Our preferred way is to hire a car unless when our tour is within the city limits. Driving is not difficult and even with a car with the steering wheel on the wrong side (read left hand drive Vs right hand drive), it is pretty easy to get used to….except the round about where you need some caution because the vehicles are approaching from your “wrong” side !! 
People narrate horrible stories of driving in some countries on the internet, but it isn’t really that bad. You just need to get to your teens and drive with a bit of adrenaline and that’s about it.
The other option is to join a tour program. While this is the most hassle free, it means you sacrifice your freedom and also risk last minute cancellation due to lack of passengers!
There is also the option of driving caravans (RV in US English) if primary intent is to do camping.