It depends what you would like to focus on: historical sites, mountains, country side?
First, don't rent from Switzerland. It will be more expensive.
Germany or France or Austria will be more attractive from a cost point of view.
Possibly, arriving in Germany and renting there. Then, make an Alps tour in Austria and some of the mythical passes in Switzerland. Also the entire Austria-Italian alpine section by the border is stunning. Depending on how much time you have, make a loop via Slovakia?
For really good historical places, you could consider the Loire valley in france which has a nice castle collection and worth a look. If you are into gastronomy, then the Bourgogne area is well worth a look , and you could drive through the Vosges area.
To go to Venice, the best way is by far the train. It is cheap and will get you there in time.
In Venice, there are plenty of crooks waiting for tourists. So be cautious and agree on the prices beforehand.
Good luck and let me know if you have any additional questions.
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