In most cases, people play Hardcore Classic because they want to see how far they can get. It would have been nice if Blizzard would have provided an official live ranking of the current position on the server, worldwide or even among the different classes.
This task has now been taken over by the site easyding.top. There you can follow the current race and the rankings of the individual classes.
Since a few days you can even search for your character and check your own ranking.