Arriving at Heathrow at 8 AM, what are the best train or bus options to Canterbury? What is the approximate cost and time to Canterbury?
This link should give you a starting point about options
https://www.rome2rio.com/map/London-Heathrow-Airport-LHR/Canterbury
Simple....Piccadilly line to Kings Cross. Cross the street to St Pancras station. Catch a train to Canterbury.
A little more specifically Piccadilly line to Kings Cross St Pancras tube station and follow the signs from the platforms to St Pancras International, so that you come up from the tube station directly into St Pancras.
From St Pancras for Canterbury, trains are operated by Southeastern -- https://www.southeasternrailway.co.uk/
There are two train stations in Canterbury -- Canterbury West (CBW) and Canterbury East (CBE). CBW is served by Southeastern's high-speed trains, generally with a direct hourly service that departs at 12 minutes after the hour and arrives at CBW 54 minutes later. If you're willing to tie yourself to a specific train Advance Tickets can be had for as little as £14 and and Off Peak (if you want to be able to get any departure to CBW) for £37.
CBE service usually is 1 hour 40 minutes with a change.