How to allow anonymous profile editing on Wordpress
the above should all be fine though that looks like a Drupal link. So if you want people to get a confirmation email when they pay for membership that contains a checksum link to a profile then I would suggest using a Scheduled Reminder triggered off a change of Membership status, and include 

WordPress: http://www.myorganization.org/?page=CiviCRM&amp;q=civicrm/profile/edit&amp;reset=1&amp;gid=N&amp;{contact.checksum}&amp;id={contact.contact_id}

where N is the id of the Profile you have set up with the fields of 'contact related' data you want them to edit.

Check your links here