Hi Deepak -
That budget should allow very comfortable, but not luxurious accommodations and comfortably cover travel and meals, plus sightseeing costs. Even if you seek out cheaper lodgings, they will be clean and comfortable.
Early September is a good time to visit the Alps, so I would include them in your plans. There are many places to do that. The Jungfrau region (the Bernese Oberland) is the most famous, but other mountainous areas are nice, too
In the Jungfrau region, many towns are car free, and public transport is the only way to travel.
Arno has suggested that you use public transport for the whole trip. That is a good idea. If you are uncertain,after you plan your itinerary, you (and we) could look at it and see if anything suggests renting a car.
I have visited Switzerland many, many times, and have developed a pattern of travel that uses inns in the countryside or suburbs as places to sleep. I often walk on trails that are most easily reached by car. And, some are in out of the way places, where a bus might only run 2 or 4 times per day. But, even those can often be reached by bus or train.
So, for that kind of travel, a car becomes useful, because of flexibility in places where most tourists do not go. You don't need a car to see grand scenery. Of course, you can stop a car to take a photograph. ;-)
Even with a car, I spend a lot of hours on the trains. And, a first time tourist almost always goes to places with frequent train and bus service.
Let us know where you will be going, after you do some planning.