If you want to install Wordpress into a development area of your website, I would recommend simply installing Wordpress on a subdirectory of your domain, (i.e.
http://yourdomain.com/wordpress/ ).
Once you have gotten Wordpress setup how you would like it, you can simply delete the contents of the root directory for your domain name, then move the contents of the 'wordpress' directory that you created to the root directory for the domain. After moving the contents of the Wordpress directory to the root directory for your domain, you would need to adjust the Wordpress configuration (in the MySQL database) to use the new directory instead. This can be easily done by following the steps at
http://codex.wordpress.org/Changing_The_Site_URLAlternatively, instead of moving the contents of the 'wordpress' directory to the root directory of your domain name, you can simply redirect requests for your domain name to the 'wordpress' directory. Here is a link to more information on how to redirect your domain name to the 'wordpress' directory:
http://www.widexl.com/tutorials/mod_rewrite.html#redirect_domain_dir . The mod_rewrite settings would go into the ".htaccess" file on your account.
The root directory for your domain name (on the Linux hosting plans - Basic, Business, Starter, Reseller), /public_html would be the root directory for your primary domain. The directory for your addon domains would be dependent on what you set when adding the domain name to your account (stored within the public_html directory, i.e. /public_html/addon).