Travel from Vienna to Lausanne in April

Best will be the one you pick after you have the data upon which to make your decision, based on your sensitivity to price and what you would like to experience on the way. Cheapest is likely to be hitchhiking, as long as you are unharmed. Next would probably be a cheap non-changeable train ticket bought when it first goes on sale. A cheap airline next (Skywork Airline, under €150 direct to Bern then train), and a normal airline last (SAS, near €200 12 hours via Copenhagen), - with a car rental somewhere up at the the expensive end because of the huge international drop charge, the tunnel tolls and both a Swiss and Austrian Vignettes. To say nothing of US$9.50 a gallon fuel (a bit less in Austria, more in Switzerland. Fastest is likely a flight - under 2 hours flight time to Bern with Skywork, then train; The SAS is 12 hours to Geneva via Copenhagen then train. Car 11 hours on the road. 10:04 by train with a 12 minute connection in Zurich.
Hitchhiking could take days or more, who knows.