Hello from Wisconsin,
I bet you have a Czech connection in your DNA. A wonderful place to go. Eat roast duck, garlic toast, and dark beer (Cerne Velkepopovicki). Austria a bit more polished and filled with tourists. Hungary...what fun. How many Z's can you put in one word?
Driving...I have been driving in Europe for decades. At least the continent uses the right hand side to drive upon. So that is good news. Unless you really want to drive through the countryside at your leisure (which is one of the great pleasures of rural Czech and Hungary) the trains in Europe are clean, quiet, and often. I needed to get from London to Bristol, England. I looked up when THE train might leave London. Well how about every half hour? Now Bristol is a big city so don't expect every half hour every where.
Driving continued. Having a car means having to park a car each night. European cities were built for walking not for cars, and especially not for moving cars and parked cars, there just isn't enough room between buildings. I now make sure the place I rent has reserved parking and I learn the extra cost, additionally I find rentals with the easy access from the highway way. Even so, in Granada I got hopelessly lost as the street I was using went underground and I missed my turn. A helpful guy hopped in with us once I explained I was lost and he rode with us until I was reoriented. People are great.
Driving continued part 3. Rent your car from a location that is easy to escape the city. Once again, I thought Foch Avenue in Paris was far enough out to make getting to the countryside easy. Whoooops! Lived to talk about it. And make sure you check how easy it is to return. Clermont-Ferrand in France was a nightmare for returning the car. Returning at an airport is usually pretty easy as the return rental parking lots have sign posts that you follow from well out of the airport mess.
One more. Driving in more than one country requires getting prior permission from the rental company. We are lead to believe that there is some unity in Europe but car rental is a bit chunky, this company permits Czech and Hungary the next doesn't. Make sure your rental agreement has it written on the contract that the car is permitted in the countries you plan on visiting.
Many of these concerns can be handled by Autoeurope, a car rental consolidator.. They have been excellent for me. Great recommendations of where to rent. How to handle multiple countries.
Notice I haven't once said, "Danger danger Will Robinson!" If you are a decent driver, you should be fine. As someone else said, the first hour. Driving the country roads is such a great pleasure it worth the hassles of the rental. Stealing into small rural villages at 10 mph. Finding the cafe or coffee shop, what a joy.
One last thought. Fly in, spend the night or two or three, then pick up the car. Don't pick it up while jet lagged.
The Czech Republic. Here is a thought. Fly into Prague. Spend a few days. Take the train to Brno. Spend a night or two and then rent a car to go to Olomouc and see the beautiful countryside of Moravia. Then drive back to Prague or Brno. If the countryside is not your goal. Trains connect these three cities often.
September is a great time to go. Three countries is too much for me these days. I understand your sense of urgency because this is trip #1. Cut it to 1 and 1/2 countries. You will enjoy yourself much more.
I rent apartments through booking.com, but hotels may be best for you. Safe? Europe is safe, not every nut job has a gun in Europe. . Pick pockets can be the problem.
Rural roads are slow roads. So once again, you might want to limit yourself to the Czech Republic. A slow road slows you down and then you start seeing things to visit. Each town has something, the old castle, the village church, a stone bridge, a museum,...
wayne iNWI, lovely snow fall today.