National Express for me, usually quicker than any other route, and I've certainly tried them all in my time. It goes more or less door to door, ground floor at LGW, arrivals level in LHR. The drivers know the short cuts and know about congestion via their colleagues and central control. Rarely crowded and generally a fairly comfortable spacious seat.

Cheapest will be a taxi if you are 3 or more in your group.

(Rats, now got that Divine Comedy song going round my brain....)