It's very easy at Paddington now the Circle Line is no longer circular. The westbound Circle Line or Hammersmith & City trains from Liverpool St go to Hammersmith, and at Paddington they stop at platform 15 in the main line station. (There is another part of the Circle Line underground at the other end of the station, which is for trains going round the loop to High St Ken and beyond, or the one stop to Edgware Road where they terminate and reverse.)

So you just have to get off the train, go up the steps to the footbridge and walk across and down to platform 6 or 7 to get the Heathrow Express. It's very quick indeed especially if you only have hand luggage.