Thanks UKTravelBear for the info! ^
So I should be able to buy a ticket from LGW to London Victoria on the Southern (First Capital Connect?) service, including a travel card (Zone 1-2?) for that day, for 16 GBP? That can be done at the Gatwick station at the Southern/First Capital ticket office? If so, that'd be a great deal!
For the Sunday I will just buy a off peak all zones ticket (need to go to the Docklands) through Visit Britain.
What do you recommend for the return on Mondays? So I just need a single ticket from Earls Court to Victoria on the Tube and then a trainticket to LGW. Buying a Travelcard for that day does not seem worthwhile. I was thinking to just buy a cash single (4,70) for the Tube and buy a single trainticket for the train online in advance. Unless there is a better option.