Our team mainly travels by train, so we aren't big experts in car renting, thus we will only give couple advices about train options and then it will be your choice - either to go with trains or rent a car.
Geneve-Venice: SBB offers special discounted ticket for travels from Geneve to Italy, so if your purchase those in advance so you can get rather good quote. For instance Geneve-Venice for only 45 CHF or Geneve-Milano(from Milan to Venice you can use domestic Italian train) for only 30 CHF. You can check discounted tickets for your dates here -
https://www.sbb.ch/mct/wi/shop/b2c/pipSchritt_2.doIf you travel before September 5 you can as well consider use of SBB Supersaver ticket from Geneva till Italian border (
https://www.sbb.ch/mct/wi/shop/b2c/adw.do?4004), then domestic ticket to Venice. Tickets in Italy aren't that expensive, so you can travel from Swiss border to Venice for not more than 30 euro, in some cases even for 15 euro etc.
Venice-Vienna: discounted tickets start from 29 euro (
http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=c79686605528a110VgnVCM1000003f16f90aRCRD). You can as well travel over the border to Villach and then use OEBB group pass (allows travel through out whole Austria for the whole day long).
Vienna-Prague: easiest part of your itinerary, just buy discounted 29 euro tickets in advance from OEBB website (
https://ticket.oebb.at/bin/frame_ticket.pl?ticket=jticket.pl?ABBFSEL=8101865&ANBFSEL=5400201&LANG=EN)
Prague-Geneve: cheapest way here is to use discounted ticket for CNL train Prague-Basel (from 29 euro) and then just travel from Basel to Geneve on Swiss domestic train. Other options is daytime from Prague to Zurich (same 29 euro), then again domestic till Geneve.
In terms of cheap, efficient etc. routes... well, most of the discounted tickets are sold for specific routes and trains, so you don't have any choice there. In case you want to travel with routes different than those for discounted tickets, then you will need either to pay more for the full fare tickets or rely on group rail passes (available for Austria and Czech republic).
It is worth to mention as well that Venice, Vienna and Prague can be visited cheaper, if you can switch the sequence of cities from Geneva - Venice - Vienna - Prague - Geneva to Geneve-Prague-Vienna-Venice-Geneve.