Most convenient ticket option for a weekend in London via Gatwick

Is there a single ticket I can buy at Gatwick that would cover the whole shebang?

Yes. When you arrive at Gatwick, for £105.70 you can get a Gatwick Airport to London Travelcard Zones 1-6 Standard Class Adult 7 day Season Tickets (Travel is allowed via any permitted route.)

This allows you unlimited travel on any train (including Gatwick Express), between Gatwick and London AND on all modes (rail, tube, DLR, bus) within zones 1-6 for seven days.

Note that if you are prepared to restrict your choice of train between Gatwick and London, you can reduce this price to £92.60 (Southern only, NOT Gatwick Express) or £81.00 (Thameslink only, slightly slower trains but not much less frequent. Note that once your Thameslink train has taken you into the London zones, you can then use any trains).

Irritatingly, however, these days even a 7 day season requires a photocard - there will be photo booths at Gatwick if you don't have spare passport-sized photos with you. There's a form to fill in which the ticket office can provide.

In addition to the answers above, you can now use Oyster cards, contactless credit or debit cards, or Apple Pay from Gatwick Airport on Gatwick Express and other regional lines into London.

From January [2016], passengers travelling between Gatwick Airport and London will be able to pay as you go using contactless payments and Oyster. The new payment methods will be available for travel between London and Gatwick Airport on Southern, Gatwick Express and Thameslink services. Five other stations along the route - Horley, Salfords, Earlswood, Redhill and Merstham - will also benefit from the up-to-the-minute pay as you go ticket technology.

This will mean more convenience and flexibility for commuters and visitors, with improved value for money in many cases, and reduced crowding at stations. It will also allow seamless onward connections to London's transport network and National Rail services.

More info on TfL's website.