Travel from Heathrow to Canterbury-Train

Trains leave from all terminals. T2 and T3 are in one place, the other not. so there are three stations, "T2+T3", T4 and T5.
Whichever terminal you arrive in you can catch a train into London.

There are two rail lines from London to Canterbury:
1) The classic line from Victoria station.
2) The more expensive High Speed line from St Pancras.

You choice which route you take. You can get from all Heathrow terminals to either station by tube.

There are no direct trains from Heathrow to Canterbury.

If you don't mind public transportation, you can take the Underground (tube) from Heathrow to Kings Cross/St. Pancras and then get a train to Canterbury. The Underground station at Terminal 3 is easy to find. There is only one line (Piccadilly line) that goes to Heathrow so you don't have to worry about taking the wrong one. And, since it is the first stop, you will probably get a seat.

Other will tell you to take the Heathrow Express to Paddington, then the underground to St. Pancras and then a train to Canterbury. This will cost you a lot more and involves more transfers. And a lot more up and down stairs.

After a long flight, I would think the easiest way is best.

I would take the underground into central London and you will get a seat as you will be getting on at the start of the Piccadilly line.

You can head to St Pancras for the more expensive, faster trains or you can head to Victoria, Charing Cross, Waterloo East, London Bridge or Cannon Street stations for the cheaper, slower trains. The route from St Pancras and Victoria isn’t as nice as that from the other stations IMO.

If you are heading to St Pancras, change at Green Park onto the Victoria line. This is a busy station and you will have to negotiate steps between the lines.

I would take the Piccadilly line to Hammersmith and change onto the District line, which just involves walking across the adjoining platforms, so no steps. Take this to Embankment. Exit the tube station and walk up Villiers Street for 1-2 minutes and Charing Cross station will be on your left. For trains see southeasternrailway.co.uk.

Why take the incredibly long walk to the Victoria Line at Green Park when the Piccadilly goes to Kings Cross St Pancras as well?

Whoops! Sorry - you can go direct to St Pancras.