Geneva is a poor base for skiing. Zurich is much better, but both airports are connected to rail stations so I suggest you fly in to either then take a train to a better ski base. It is also feasible to take the train all the way from London to Zurich with a change in Paris. The train system in Switzerland is fantastic (as are the post buses). If you want to ski lots of different ski areas using public transport, Lausanne, Sion, Serre, Chur and Interlaken make good bases. For beginners Wengen, Grindelwald, Arosa or Flims are good choices of places to stay which you can get to by train. Flims is also probably the best resort for boarders. For experienced skiers Engelberg, Les Diablerets, Champery, Murren, Andermatt, Davos, Klosters and St Moritz are easily accessible by train. Zermatt is possibly the best all round ski resort in the world and is also on a rail line. If you want to hire a car, definitely think of staying in the Rhone valley to savour Nandez, Val D'Annivers, Saas-Fee, Villars, Leukerbad and Crans-Montana (although you can also get to these resorts by post bus from the valley). Flims, Zermatt, Verbier and Engelberg have good apres ski as well as good skiing and snowboarding. Visit www.myswitzerland.com and
http://railaway.rail.ch/snow-n-rail/ for more.