Cheapest option to travel around Switzerland

Hi,

I need a suggestion about the cheapest option to travel around Switzerland. We (2 adults) will be only two days and two nights there and we would like to visit as many places as possible.

Our itinerary would be
August 19: Arrive Geneve Airport in the evening.
August 20: We want to travel from Geneve to Zurich following the same way than the Golden Pass line (visiting Montreux, Interlaken, Lucerne, Zurich). Which would be the cheapest option to do it? Are there other (and cheaper) trains that cover that way? Is it possible to get a discount for Golden Pass Tickets?
Is the Swiss Half Fare Card a good option for us?
At the end of the day we have to return to Geneve because our hotel is there.
August 21: We want to visit other cities near Geneve like Lausanne and Nyon. Once again, which would be the cheapest option to do it?

We are also exploring the possibility of renting a car. This would be cheaper than the train?

Please, help me! This is our first time in Switzerland!
Thanks!

Hello Annika thank you for your answer!
I understand what you meant, it's only that I really wanted to go to Lucerne! :( Maybe next time!
So I think I will visit Montreux-Laussane on Saturday and Nyon-Coppet on Sunday.
It is more realistic, isn't it?

Thanks a lot!

Hi momi0701. Yes, that's definitely more realistic. I understand that you want to make most out of your trip, but Geneva, the lake and its immediate surroundings are beautiful as well. You won't get bored visiting Montreux, Lausanne and Nyon. Have a great time!