We arrive at Heathrow about noon on 08/14. We are headed directly to Canterbury. I know advance tickets are less expensive but I am not sure what time we will get to the train station based on actual arrival/customs/etc. How can I purchase a ticket that would be good anytime on 08/14? Which site should I use to purchase tickets? Thanks!
Start at the website for National Rail and go to the Planner. Plug in your route and day and the earliedt reasonable tine. It will return a list of trains from that time forward - all train companies, all routing. You can expand any of the trips to see all of the fare options. Generally in standard class there are 3 major buckets - advance for a specific time (if available); off-peak if the train is not during peak hours; and any time.
Having said that, uf you are not committing to a specific journey with an advance ticket, you can just buy the appropriate ticket at the station when you get there.