Heathrow called "The busiest airport in the United Kingdom" You would experience this upon arrival.There is an rail link connecting Heathrow and London city. This could work out cheaper and convenient. This Heathrow Express has free wifi too.
The Oyster card! A boon to ease travel in London.
Hop in and hop off the undergrounds, buses all with this magical card. This will definitely ease all your local travel concerns in the city.
There are several offers on buying this card with the London Pass.
London Pass - a sightseeing pass for tourists. It consists of a smart card which entitles the holder fast track entries to several attractions (Definitely not all ;)
You could choose either of these depending on your duration of stay and travel needs while in London.
Once you get your Oyster card in place you are unstoppable. Explore London by bus,underground or walk.
Notes to help you plan your days in london better.
Piccadilly Circus,Trafalgar Square,Big Ben,London Eye could be your plan for one day.