The question is if you have a UK debit card or not. If not UK, then would suggest oyster, as believe one would likely incur bank charges for foreign, non UK Cards, like in any transaction.
We prefer to use oyster, have them registered and can check on line usuage, handy as sometimes have been overcharged, so then apply for refund on line. We do not check often, but if suddenly see usuage is more than expected then check.
re Overground usuage - there is a daily maximum charge for oyster* within greater London area, charge varies depending which zones you use & if you have been in peak time or not Monday to Friday. Believe the same * applies for all contactless card payments. Many if not all London Overground (BR) trains are included in this Oyster daily charge.
Gatwick - Not sure if Gatwick express is different, but other Gatwick trains to London, if for example you knew you would be using a daily charge ticket, then you would I think be charged from edge of whatever zone you reached the daily charge for, a usual example would be zone 6, though I presume would be the same if you reached target for zones 1 & 2. Probably for many travelling, they do one way journey on arrival so would not be in that category. Though possible more complicated one might have to buy the daily charged ticket before buying the Gatwick ticket, I am guessing that bit.
Ticket offices, London Underground (Tube) no longer have ticket offices, not sure if perhaps Heathrow does, as an exception.
If you have a problem with using the oyster machine in a London Underground station, there should be a member of staff somewhere around who you can ask for assistance.
Many Overground stations still have ticket offices with limited hours.
Oyster machines are in London Underground stations as well as Overground stations. I believe one can buy an oyster through the machine as well as get a refund and return the card that way - it may be that you have to register all your cards online, then apply for return of them as well any money on them, before you can return the cards into the machines - I am not sure.
There are also some shops that you can top up your oyster card, you look for the oyster card on their shop windows, a bit like if they sell lotto/euromillions tickets.
We do have several spare oyster cards, find them very handy for friends visiting London from Outside UK.
BTW, believe there is also a phone appliance you can use to pay, but have never used that system, presume it works the same way.
Finally when using the contactless, whether oyster or another, make sure there is only one in your wallet or whatever when touching the Oyster thingie in and exit, as can either cause double charge or affect the daily Top charge, example if it took payment from one card for one transaction /journey, but took the payments for the other journies from another
ps: Tourist note, there are some London attractions that offer discounts with an oyster card usuage, not sure if that would be the same for other contactless payments