To stop the "Welcome Guest" message on the index page. Log In as admin and go to:
Configuration > Layout Settings > Customer Greeting > Show On Index
Set it to 0 (zero). This will stop displaying the message.
If you want to change or delete the message, FTP to your server and download the index.php file located at:
Make a backup copy of the file.
Open the file in a text editor. Find the section:
define('TEXT_GREETING_GUEST', 'Welcome < span class="greetUser">Guest!</span>
Would you like to <a href="%s">log yourself in</a>?');
Delete or change 'Welcome Guest! Would you like to log yourself in?'
Only change the displayed text. Don't change the embedded tags.
Upload by FTP the modified file and overwrite the existing.