Oyster card vs off-peak fares
That's the main decision you have to make. My own recommendation would be to use Oyster.
the maximum charge on the Oyster is 11GBP per day?
Sorry, no. GBP 11.00 is the maximum charge for travel within Travelcard Zones 1-5. Zone 1 is central London. Zone 5 includes both East and West Croydon, so you would not expect to exceed GBP 11.00 for each day spent in London. A minor exception would be a trip to the very edge of the London Zonal area, for example Hampton Court Palace which is in Zone 6, in which case the Zone 1-6 daily cap of GBP 11.80 would apply.
Oyster has been extended to Gatwick Airport in recent months, but the zonal area has not been changed and travel to and from the airport is charged separately and does not count towards the zonal cap (although, as
MikeWh explains in posts 10 and 12, it does have its own, higher cap).
Gatwick Airport - West Croydon single fares are GBP 8.20 peak and GBP 6.60 off-peak.
Gatwick Airport - East Croydon single fares are GBP 5.20 peak and GBP 3.00 off-peak. A peak journey is one in which the initial Oyster touch-in is Monday - Friday 0630-0930 or 1600-1900.
We are just bringing carry-on rolling bags, and small backpacks, so the journey from East Croydon to West shouldn't be too difficult.
Good. In that case, I recommend rail Gatwick Airport - East Croydon, then tram (if still operating) from East to West Croydon. Each tram journey (and each London bus journey) costs GBP 1.50 and does count towards daily and weekly caps.
East Croydon tram stop is at the southern entrance to the rail station, up a long ramp, not a footbridge. On exiting the tram at West Croydon, walk back from the tram stop some 70 metres to the previous set of traffic signals. Turn right into London Road. The main entrance to West Croydon rail station is some 80 metres along London Road on your right, and the Fox and Hound pub is on the other side of the road.
We are arriving at night though
What time is your flight due to land at Gatwick?