What's the best mode of transportation for the least expense?

From Heathrow, the Piccadilly Line. Buy an Oyster Card (£2/journey)...

Where'd you make up that number from? It says here

http://www.tfl.gov.uk/assets/downloa...April-2007.pdf

that a single ride with OysterCard varies from £1.50 within Zone 1
(i.e. Central London) to £3.50 if you go from Zone 6 (i.e. Heathrow)
to Zone 1.

or a day Travelcard ....

With an Oyster card you pay whichever is cheaper, the single fares or
a "capped" price for the day. Others here will be more familiar
with the details.
--
Mark Brader "I'm not good in groups. It's difficult to
Toronto work in a group when you're omnipotent."
"Deja Q", ST:TNG, Richard Danus