The following are the things should be done before making your drupal site public
1) make sure your /sites/default/Settings.php is writable by system only
chmod 644 /sites/default/Settings.php
2) make sure your default install folder has .htaccess to enable clean url's. if its already there enable it.
refer General#Clean_URL.27s
3) if you are going to make the site public, make sure you disable new user creations by anonymous.
make it by enabling new user creations by administrators. you can change the options in User Management section.
If you want to have new user creations by anonymous , then installing capatcha module is good thing
4) for extra protection remove install.php file from the main directory.