I recently landed at LHR with LGW flight the next day. Took the national express bus, it was pretty good. I've done the train connection (2 trains plus tube) and it isn't that great - probably actually takes more time.

Based on my travel history I'm more familiar with hotels around Gatwick. This time I picked the Ibis at 50 quid. Nice pub next door, free ride from airport, city bus back to airport.