Heathrow or Gatwick?

All things being equal, I'd say Gatwick.

Note that there are 2 stations in Canterbury, East and West, so do check which one is best for your destination.

Agree with Frank II. Gatwick is much more user friendly, and would be my preference.

I don't think it matters.

From Heathrow, it's a straight journey to King's Cross/St Pancras, then a train to Canterbury West.

From Gatwick, it would be a train to St Pancras, London Bridge or Victoria, then a train to Canterbury West or East.

Note that the fast trains to Canterbury go from St Pancras. It can be quite a time difference- St Pancras to Canterbury West is only 54 minutes, whereas from Victoria is 1hr 30min and Charing Cross is 1hr 45min. It's easy to get from both Heathrow and Gatwick to St Pancras- either the Elizabeth Line from Heathrow to Farringdon and then one stop on the tube, or the Thameslink from Gatwick to St Pancras.

The airline one uses to fly into the UK will determine whether one arrives at Heathrow or Gatwick.

On National Rail you will note that trains from Gatwick to either CBW or CBE are generally 2 hours to 2 hours 45 minutes and involve anywhere from 1-3 changes, with one of the services changing at St Pancras. And priced from £28-£58.

For me it would be land at LHR, the Piccadilly Line to St Pancras and the fast train direct to CBW at £17.50.

From Gatwick it's pretty simple...

Thameslink to St. Pancras, Southeastern train to Canterbury West. Under two hours. One change.

You don’t say where you are flying from. It is better to get a non-stop flight from North America and that generally means you will land at Heathrow. I’d look for the best flight to London first.

A left field choice which may be appropriate. If you don't have a one stop option into either Heathrow or Gatwick you might consider flying into London City (LCY). This would probably mean flying via somewhere like Dublin, Amsterdam or Paris. The advantage is that LCY is by far the most user friendly London airport with very quick transfers through. It also has the advantage in that you would have a short transfer to Stratford International station where you can pick up the fast train to Canterbury which starts at St Pancras.

Lots of options. Lots to think about. Thanks, everyone!

Another vote for using London City Airport if you can manage it.
It really is a ‘user friendly’ airport.