The Underground or tube is a wonderful way of getting around London. However if you are travelling with a suitcase to or from the airport, it's not so easy. Many stations have long and short flights of stairs up and down all over the place and no elevators (lifts). However,it is possible by visiting the London Underground web site, to find out which stations have lifts (elevators, This will make your life much easier. Big suitcases on the "moving staircases", (escalators) are a real hazard both to you and others! I lost hold of a suitcase last year and almost demolished a row of fellow travellers below!
You can also get special passes to the London underground (the tube) http://www.londontravelpass.com/prices.asp?gclid=CLTjqOCp45MCFRUasgodvwUKZg
A map of the underground will come in handy.
By the way, the Underground has some very interesting posters on the walls, although sometimes it's difficult to know what they are advertising!