You now don't need an Oyster Card to get Oyster rates of pay: you can use a contactless debit card, see here
As long as you use the same card for each journey every day you will benefit from the capping system. Basically the card calculates when you reach the daily rate for a day tarvelcard, for example, and cpas the exoenditure. See here. But you must use the same card for every journey.
Bus fares paid for with a contactless card are the same price as using Oyster see here.
So using a card would avoid the hassle and initial expense of getting an Oyster, and getting it topped up.
You can't use cash on buses now.
You have to pay £10 for a Zip Card (as they call the free travel for 11-16's cards) and have the passport etc, so it probably isn't worth your while, but you can buy a Child Rate paper travelcard. see here
There is a good network of buses from Crystal Palace, but they can take a while to wend their way through S London especially if you come home at rush hour. Stroll across Crystal Palace Park (turn sharp Left out of the campsite gate and cut through into the park instead of turning R out of the gate on the the main road - the helpful campsite people will advise you) down to the Crystal Palace station and ask there about routes and timetables. You can get the overground direct to London Bridge (for attractions such asn HMS Belfast, Borough Market, Globe, Tate Modern along the river walk etc), or else go the other way and access the tube network at Blaham.
Otherwise get the No3 bus as far as Brixton and then hop on the Victoria Line at Brixton.
Crystal Palace Park is interesting and quite lovely - nip into the little museum and research the history of the Great Exhibition etc, there is a small city farm / zoo, the dinosaur park etc. Not what you will have come down to London for, but nice to stroll in.