PAYG on Oyster caps to the lowest fare available for your travels. If you use Oyster to travel from LHR to central London (zone 6 to zone 1) then take two more Underground trips that day you'll not pay the zones 1 - 6 off peak cap of £7.50 but £6 (£2.40 for the off peak trip from Heathrow plus two £1.80 fares within zone 1).

The one day off peak cap for travel in zones 1 and 2 will be £5.60 for your journeys on Thursday and Friday; rather than pay £4.50 for the journey from central London to LHR on Saturday the Oyster single fare is again just £2.40.

£25 should be more than enough for your needs. You will receive the £3 deposit for the Oyster itself plus any unused PAYG pre-pay when you hand in the card at an Underground station at the end of your stay in London.

And you say you'd 'like to check out London Bridge/Big Ben at night'. Since London Bridge is a rather dull concrete structure I suspect you mean Tower Bridge, which is the business. Westminster Bridge at night (and in the daytime) offers very good views of the Clock Tower with Big Ben tucked up inside; BB is the bell rather than the clock itself.