England - Stratford International Train Station

When the train leaves St. Pancras for Canterbury, the first stop is Stratford International.

Neither the Heathrow Express nor the Elizabeth Line go to St. Pancras. They go to Paddington and then you can get the tube to St. Pancras.

Or, just take the Piccadilly Line from Heathrow to Kings Cross/St Pancras and then get the train to Canterbury. That's what I would do.

The Elizabeth line goes the Stratford station, which is 1/2 km from Stratford International, so that is a 15 minute walk according to Bahn.com. The Elizabeth line goes every half hour to Stratford station from Heathrow and the South Eastern direct train to Canterbury West goes every hour and there could be extended wait time at Stratford International.

I know the Stratford area very well. Not every Elizabeth line train goes to Stratford. The walk from the Stratford Station (Elizabeth Line) to Stratford International is through the very large Westfield Shopping Mall. It's always crowded and dragging luggage through is no fun.

It will take about an hour to get from Heathrow to Stratford via the Elizabeth line. Then the walk through the mall. (You can walk the longer way around the outside perimeter of the mall if you want but it takes longer.)

It will take about an hour to take the Piccadilly line to St. Pancras. All Piccadilly line trains go to Kings Cross/St. Pancras. They run every few minutes. St. Pancras is a much nicer station to wait in than Stratford International.

The Elizabeth line fare from Heathrow to Stratford is 15.10 GBP. The Piccadilly line fare from Heathrow to St. Pancras is 5.60 GBP.

There is only a 10p fare difference on the train from London to Canterbury if you get on at Stratford.

The other option, as opposed to walking, from Stratford station to Stratford International station is to take the DLR- the Docklands Light Railway one stop to its terminus.
I think the St Pancras route is the better route.
The Elizabeth Line with the switch of train for either station is only marginally faster than the direct tube to St Pancras.

The fare Heathrow to either Stratford station is £13.30, not £15.10.

I'd agree that the walk across the Westfield Centre between the two Stratford stations sounds great with all the shops but actually it is somewhat hard work especially humping baggage.

I prefer to use the train feeling of the Elizabeth Line over the tube of the Picadilly Line - probably there are good reasons that the Elizabeth Line is the busiest line in London now - but I'd suggest changing at Farringdon for the short run up to Kings Cross St Pancras and joining the Javelin service where it starts its trip rather than standing on a wind swept and perhaps wet platform at Stratford. I've done both several times and I know which I prefer.

When you join the train at St Pancras you have all the food outlets at St Pancras and Kings Cross (across the lane) to stock up for the adventure (eating on trains is perfectly acceptable, just not too whiffy please). The platforms are actually upstairs, most of the way north on the east (Kings Cross) side of the station, there are lifts and escalators and stairs. All under cover so no wind and no rain. The train stays in the station for several minutes so easy to choose a seat or two, put up your luggage, and settle in. In my opinion that's much better.

Use the tfl.gov.uk site. You can edit your preferences as to fastest way (Heathrow Express to Paddington to Circle Line to St Pancras in 52 minutes costing 27.70 GBP off-peak). Or fewest changes (Piccadilly Line to St Pancras in 71 minutes costing 5.60 GBP anytime).
I'd go with the Piccadilly Line and save the 22.10 for your traveling snacks.

This is exactly the kind of detailed information I was hoping for. Thank you all, so much.