The *cheapest* way, if you have a Z1-2 pass, is to take as many TfL buses as you need from your origin, with the final bus being the 405 from Croydon to Redhill, as this will not cost you anything extra.
Then the Oyster/contactless fare from Redhill to Gatwick is £4.60 peak and £2.60 off peak.
There is also Metrobus route 100 from Redhill to Gatwick for £2 (no Oyster, pay cash, contactless touch-in/-out, or possibly app).
If you want to do it all by train, then it's cheaper to split at East Croydon, which you need to do by exiting the station and re-entering, you can use the same card/device and don't need to wait before turning around.
However this involves a long-ish walk along the ramps at the southern entrance, or up and down stairs/lift to the footbridge at the northern entrance, to get from the platforms to the barriers.
(Edited to remove incorrect info about tram validity)