The "Plain text" input format cannot be disabled for any role. Even if you disable the permission to use the plain text format for a role, users with that role will be able to use the plain text format.
To allow all users to use the full HTML format, you need to:
- disable all the input format, except the plain text format (which is the only one you cannot disable), in admin/config/content/formats
- rename the plain text format in "HTML." You cannot rename it "Full HTML," or "full HTML" as Drupal will report you that a input format with that name already exists.
- change the settings for the input format as shown in the following screenshots, which show the settings before and after the changes.
(PHP evaluator will be visible only when the PHP filter module is enabled.)
You can also disable the "Convert line breaks into HTML" filter, if you want. In that case, the new line characters will not converted in
<br /> tags, and the text will not be wrapped in
<p> tags. I would also disable the "Convert URLs into links" filter, which is the filter that changes texts like
http://example.com in http://example.com (as it is done in SE sites). I would keep enabled the "Correct faulty and chopped off HTML" filter, which is the filter that fixes the missing closing tags; this avoids that a user can mess with the HTML layout of your site by leaving out a closing tag, such as
</b> that would render all the page in bold, or
</table> that would seriously mess-up the layout of the page.
To notice that the disabled input formats will not be visible anymore in the settings page, but the "filter_format" table will still contain the data about those input formats; that is the reason you cannot rename the "Plain Text" format as "Full HTML." That database table is also the table that you need to alter, if you want to change the machine name of the input format; in that case, I would first delete the rows for the input formats you don't need.