You can get the same "Pay As You Go" fares either with an Oyster card, or with a contactless debit/credit card. Both options are subject to the same caps -- that is, after you've reached a certain total price in the same day (and on the same card), travel in the same zones is free for the rest of the day.
If you already have a contactless card and your card issuer doesn't charge fixed per-transaction fees for international purchases, using that will be much more convenient than Oyster.
On the other hand, you might be able to benefit from Oyster if your card has high fixed fees. But for a two day-visit, that will most likely not be worth it. Transport For London will combine all your travel in a single charge each day, so you'd save at most two transactions, and unless you plan for extra time to get the card deposit and leftover charge on the Oyster refunded when you leave (at have something to spend the refund on!), that can easily eat up whatever you save on bank charges.
The precise fare caps depend on which zones you travel in. You can find the caps at https://tfl.gov.uk/fares/find-fares/tube-and-rail-fares -- ignore the big "Caps and Travelcard prices" link that leads to a clunky one-by-one query form, and instead scroll down to the "Adult caps and Travelcard prices" PDF link further down. The daily cap for zones 1-6 (which covers the center of the city and all the way to/from Heathrow) is £12.80.
PAYG is the only way to pay for bus travel, and is also the cheapest way to travel on the Underground.
You can now pay for Heathrow Express with the same Oyster/contactless options, but it uses special fares that are very expensive and not included in the caps. Unless you're in a particular hurry, just take the Piccadilly Line from the airport into the West End.
