Move "Log in or Register to post comments" to the bottom of the page
You need to change the fields order in Manage display /admin/structure/types/manage/page/display (replace page with your content type machine name e.g. article). Change Links after Comments.

If you don't want to show this information in lists, then in teaser view mode drag links under Disabled. Note that this will also disable the default read more link. If you don't have teaser tab available, then you need to enable it under Custom display settings.