Heathrow to Sheraton

Good deal: go to central bus terminal and take 75, 76 or U3 bus for free (and take a five minute walk).

Good deal: arrange w/hotel for a car, £10 between hotel and terminals 1,2,3.
Not a good deal: Hotel Hoppa bus, £4 per person, takes as long as the free bus though gets you to the door of the hotel... Eventually.