If you are implementing on your project only three user levels then I suggest using middleware. This would be the easiest way just be defining on users table the user level (admin, moderator or user). If your users have to do more specific tasks and they have to have predefined permissions on database than you have to use also the policies (or gates).
https://laravel.com/docs/5.5/authorization#gates
https://laravel.com/docs/5.5/authorization#creating-policies