LPV/LP approach (RNAV with WAAS): What is actually the "channel number"?
This pdf by Jeppesen provides the meaning:


  WAAS Channel Number, unique to each airport, and  Reference Path
  Indicator (RPI), which is made up of the letter “W” plus two or  three
  characters representing the runway number.  These are shown in both
  the Briefing Strip (chart heading) and plan view.


So the Channel Number provides the airport, and the RPI provides the runway number as well as the specific procedure. The combination of the two of them provides a specific approach at a specific airport, in much the same way that the title of the procedure on the approach plate is only meaningful if you combine it with the airport identifier. 

As far as what you need to select in a particular avionics package, that depends on the design, but you are correct that it doesn't affect how it processes the GPS / WAAS signals.