The second most populous city in Switzerland after Zurich, Geneva is a great tourist destination. As all your dream destinations (Vienna, Salzburg and Liechtenstein) lie on the main route between Switzerland and  Austria, I think train is the best mode of transportation to enjoy the serene natural beauty all around and explore the majestic beauty of Alps. As Switzerland, Austria and Liechtenstein are bordering nations and neighbours, it is better to opt for the rail service (Eurail). There are a number of cheap offers, which you can avail to visit these bordering countries. 

Eurail (Source: miss_rogue)

Geneva to Vienna (Eurail) (22nd Sep-24th Sep):

(Source: Eurail (Geneva to Vienna)

Bookings: Book Your Tickets Here

Geneva to Salzburg (25th Sep- 27 Sep):

 (Source: Geneva to Salzburg (Eurail Pass)

For Bookings: (Austria- Switzerland Select Pass)

Note: Austria-Switzerland Pass is valid for travel to Liechtenstein.

You can get train schedules and book tickets to different destinations on the Swiss website : sbb.chexe

I think traveling by rail is just the right option for you, as you will have to pay exorbitant fares if you prefer traveling by air. In my view Eurail option is the best one. You can start from Geneva at night and spend a 2 Days exploring Salzburg, from where you can proceed to Vienna(2 Days). While coming back, you can take a train to Liechtenstein. This way you can save money and cover these three bordering countries at your own pace . If you need any further help, you can always get back to us. Till then, keep smiling and keep exploring.

Cheers!

Rakesh