I have lived in Saudi Arabia for five years, Germany for four and since getting the kids through college and reaching retirement in 2010, we have traveled extensively.
When we lived in Germany, we had to budget our travels, but we could just hop in the car and go where we liked. We did a lot of winging it. We had a couple of experiences that warned us about having no advance planning, like showing up in a city were a festival was going on and all (I mean ALL) hotels were booked. We had to drive (at night another 60 miles to find a place to stay. On another trip with no plans, the city was fully booked and fortunately the hotel put us in the maid's quarters for one night, since we could not drive over the snowy Alps.
We have done bus tours, rail tour, taken trips by rail, trips by car, cruises, river cruises and more.
I enjoy planning, since it gives me an opportunity to find out in detail what is great to see while in a city or town.
We had a wonderful 4 week drive tour of Wales and England that we planned out to the day with B&Bs and sometimes day tours.
I would advise you to do some advance planning, perhaps for your first two weeks at a minimum. If you know where you generally want to go, then at least pick out the cities or towns and the key places, museums or historical sites that you want to see. If you have a computer, you can do planning for the rest of your time in Europe. One thing, beware, using wifi, even in hotels can easily lead to viruses on your computer.
Cruises are great for visiting places like the Greek Islands that are not easy to get to otherwise. For major cities like Rome, Paris, Berlin, Munich, Barcelona, Madrid, London, and more, at least pick out 3 hotels (not booking) ahead of time as alternatives that you can book later. For major cities plan on staying 4-6 days.
Be sure you have more than one ATM card to get local currency, since if a machine eats one card, you can still get cash.