Just to do some quick, indicative calculations:
First example: if you were to only travel around Z1-2, contactless PAYG for 5 days for the adults @ £8.90p/p per day would cost a maximum of £133.50. 5 days of Young Visitor discounted caps, plus £7 for the Oyster card, would cost £29.25, making for a total cost of £162.75.
Second example: if you were to only travel around Z1-2, and used a Family Railcard-discounted Travelcard for the child and one of the adults whilst the other asdults used contactless, it'd cost £160 in total. This makes it cheaper for the 15yo, as they get 60% off the already 50% discounted child fare.
Third example: the Family Railcard option begins to get better value if you're going to be travelling more widely, e.g. if you travelled across Z1-4 you'd be looking at a £12.80 daily contactless cap - thus the first example would instead cost £221.25. In that case the total cost including buying the Railcard, with everyone on Family Railcard-discounted Travelcards, would be £181.
And if you're travelling to/from Zones 5/6 the Family Railcard option cost stays the same, whilst contactless PAYG costs even more.
If mainly travelling in Zones 1-2, getting the 11-15 Zip Oyster card is almost certainly the cheapest option (it costs max £24.50 including the cost of the application) if you have enough time for it to get to you before the trip.