For Daily Tickets our best understanding to date follows:
Redhill Route stations don’t generally have “return” tickets to Victoria or London Bridge but a London Terminals ticket instead. So it is normally better to buy a Gatwick Southern only ticket to just one terminal. If you need the flexibility of multiple stations then buy the standard Redhill ticket.
However there is one ticket the Redhill Route to Victoria Super off-peak return at £9.00 is very cheap but only allows travel to Victoria off-peak and is nit usable between 16:00 and 19:03 from Victoria (19:10 Horsham is first train it is allowed upon after peak).
Also use on Thameslink is tricky question, some say they are valid as Thameslink and Southern are the same train operators but some say not. I think it would be a very mean inspector that prosecutes considering our trains have turned Thameslink only in December.
Oyster has added to this complexity. Single fares to Victoria are cheaper than Redhill to London Terminals tickets and Gatwick tickets. So if you are going just to Victoria or London Bridge Oyster works and is cheaper. If you are going to add more travel like a tube and a bus you have to think carefully.
However once you The caps seem to be £29.80 Peak and £19.00 off peak. If you are travelling off-peak it seems best to buy a paper ticket at £16.00 All-Zone travelcard from Redhill Route stations (Salfords/Horley is £17.00, same as Gatwick), especially as all but the Victoria one mentioned above would allow you to travel from 16:00 to 19:00 whereas Oyster makes that Peak time. Oyster would cap your fares at £16.00 unless you travel on anything between 16:00 and 19:00 when it’ll cap at £29.80.
It appears that Oyster also has a higher cap than Contactless for off-peak
Oyster can save you if you do limited journeys and one of your journeys is off-peak.
Also you can cut fares by avoiding Zone 1 and touching the pink readers. However on a journey I planned I found that via Zone 1 was cheaper than using the pink readers at West Brompton for off-peak journeys only : so confusing
I think you need a degree in Maths and logic to really understand all this. So that’s my best explanation as I understand it all currently. I’m sure many will find cheaper hacks – please post them if you do so everyone can use them