Heathrow is by far the best, outside of special case London City, but if you insist on the others:
Stansted has links to the centre of London but the fastest will take you about 47 minutes.
Luton can have you in the city centre in about 40 minutes by train which is reasonable, but not quite as fast as the options from Heathrow.
Gatwick has expensive options that will take about 30 minutes, plus you can take ordinary trains running on that line (which is the Brighton to London line). Of all the options outside of Heathrow, this one is the best.
Southend airport is quite distant from the city centre, so the options aren't as attractive. I'd put this one at the bottom of my list unless you're heading to suburban southeast London.
London City airport is the best of all because it's physically located in the city centre, but the only flights from overseas are from JFK, I believe, and they are expensive flights. I have flown this airport on a Zurich-London City-Glasgow routing and it seems quite pleasant.
Where in London you want to end up is going to affect your answer. When we go to London, we typically stay near a Piccadilly station, so Heathrow's easy access to the Piccadilly line is pretty tempting. It's inexpensive, and fast enough. Details are here for other readers who may be willing to use the airport.