Due to a combination of reasons that include geography, history, and what can only be described as “Englishness”, London is served by six airports. None of them are unequivocally great and none are always bad. The best airport depends on your destination/origin within London, your flight destination/origin, and the passport you carry, among others. Here is a highly subjective guide with data as of early June 2016.
London does not have a central train station and it barely has a central rail spine. Further, journeys into or through central London (roughly the Transport for London fare zone 1) are best avoided whenever possible on grounds of cost and crowding. Because of this, your London origin/destination matters a lot to which airports are convenient to get to.
The destinations of the flights also vary: you will struggle to fly out of Europe from anywhere but Gatwick and Heathrow, while smaller European airports are almost exclusively served by low-cost airlines out of Luton or Stansted.
As the UK is not part of the Schengen area, all passengers arriving from destinations outside UK and Ireland require passport control. For EU/EEA passport holders this is largely a formality and goes fairly quickly. Non-EU/EEA passport holders undergo somewhat more stringent screening, which can take a long time, particularly at airports with lots of non-EU traffic, Heathrow and Gatwick, and at peak times, e.g. mid-morning red-eye arrivals from Americas.