What is the "best" way to get from Heathrow to Earl's Court?

The Underground will probably be cheapest, and both Heathrow and Earls Court stations have lifts.

I agree with Philip.

Straight shot on the Piccadilly Line from Heathrow to Earl's Court. Cheapest and most convenient option. http://www.heathrowairport.com/transport-and-directions/underground Taking the tube allows you to experience commuter travel, get the hang and ease of using it while in London as well as glimpse at life outside London. Great city. Enjoy yourselves!

One other quick tip : at the Hammersmith stop , you can jump off the train and walk right across the platform ( a hop , skip and a jump ) to a District line train . The district train puts you on the upper level of Earl's Court station with no need for the lift or a longish flight of stairs with your bags . ( The Piccadilly line is on the lower level )

Happy travels!

Although what Steven says is true, there is no completely step free route from the east bound District line (ie from Heathrow) presently until 26 May because of maintenance. However, there is step free access from the Piccadilly Line to the ticket hall via a lift.

I stand corrected . Marco is right , there is indeed a short stair run from the District platform to the ticket hall . I forgot that the lift from the Piccadilly platform lets out at street level just past the turnstiles . Marco , Many thanks !

Well, it's unanimous, so I'm taking the advice given here and taking the Tube.
The very detailed answers have been quite helpful. Thank you to each of you who has answered!