Its straightforward to rent a car at Geneva Airport, and this will give you maximum flexibility for exploring the valley. Counter-intuitively, book a car from the Swiss side of the airport - then it will come with a vignette which permits you to use Swiss motorway - which is the quickest route here. If you're coming in the winter season, it's worth getting winter tyres on your hire car - they make life easier (and safer) on icy roads.
Or for airport transfers in the winter season, Go Massif are the best transfers operator in the valley. They're a great organisation: well maintained vehicles, professionally qualified drivers, and simple online booking.
Driving from the UK takes 8-9 hours on the motorway direct from Calais (via Rheims, Troyes, Dijon, Geneva). We often drive this route, stopping off overnight in Chablis to enjoy the local wine and food.
The nearest train station is down the mountain at Cluses. Take the Eurostar from London to Paris (Gare du Nord), and change to Gare du Lyon to pick up the TGV south to Cluses. Its about four and half hours Paris - Cluses.