"As you say, setting up a specific folder in which to create the backups sounds like a much better system, as that way the backup files are in an identifiable location and they also have identifiable/helpful filenames."
Yes, i think it's better to have them in a dedicated folder.
But if you had made automatic backups in default place before, you'll have to find a way to manually delete previous backups. Some search in this forums should give you good help.
Because the option to automatically delete older backup files (when a certain number/date is reached) only works for the (new) configured area!