It will depend on when you fly but usually Heathrow is the most expensive. For London you could use Gatwick, Luton or Stanstead. London City has some flights in from Europe but not from the US etc.
I prefer Gatwick as its much smaller than Heathrow, especially if I am coming in on an International flight and changing to domestic.
For the other airports that are international, I am guessing it will depend on your airline, when you want to fly etc. about 6 years ago