Upvote:2
If you rent a car, you will probably need a minivan. For one week you will have to foresee a budget of at least 1200 EUR (rental, fuel, toll, parking for one week) and 2000 EUR for two weeks. The roads are good and driving there is easy.
But for the same budget (and probably even less) you can also go by train. If you want to visit the cities, you won't need a car. The train brings you from city center to city center. On the specified legs you have direct trains. Fro Venice to Vienna, you can even travel over night. So you will win one whole day on you trip.
Hence, take the train. It is more comfortable and a bit cheaper. And it is fun in a group of five.
To prepare your trip, have a look a the trains tag of this site. You will find answers to questions that you may have. And have a look at The Man in Seat Sixty-One.