I have found the best ticket to get on a Saturday is a Gatwick day return with an all zones travel card included and just don't use the return portion.
Depending on the offers available it is usually valid on either First Capital or Southern Trains only ( FCC is usually cheapest) but that is only for the section between Gatwick and East Croydon where the London travel zone starts.
Its not train specific so if you are delayed at the airport you just get the next train from that operator.
I have got these tickets for under £10 but I think that they are about £13-14 at the moment.