Traveling April but see there are several trains throughout England. What’s the best from Heathrow to Canterbury via London?
Of course there are several trains throughout England, there are several different places to go to and many persons who want to go somewhere. If you want to go to Canterbury, the best is to take a train that goes to Canterbury, you can see options at www.nationalrail.co.uk (keep in mind that there are two stations in Canterbury).
There are two train stations in Canterbury (Canterbury West and Canterbury East) and they can be reached from London's St Pancras, Victoria, & London Bridge stations.
Southeastern is the train operating company for the this route -- https://www.southeasternrailway.co.uk/
Though any train operating company can sell the tickets.
Personally, for myself I would purchase for £45.20 (if my plans were to return to London) an Off-Peak Anytime Return ticket for a direct train from St Pancras to Canterbury West. Once landed at Heathrow I'd simply travel from Heathrow to St Pancras Station direct by the Piccadilly line. Travel time is approximately an hour and walk up from the tube station into the train station and take the first available direct train. Direct trains from St Pancras to Canterbury West are about 53 minutes. There are other options at a few £ less, look for what fits your needs best.