Install WP in a folder in site

You have it exactly correct. Create a directory in your existing web root and name it whatever you like, then just upload all of the WordPress files to that directory. The install path will be just like you have it: www.sitename.com/folder_name/wp-admin/install.php Then to access admin on the installation, the url will be www.sitename.com/folder_name/wp-admin

That will let you have a wordpress install in a sub-directory of your existing site, not on a sub-domain. The only caveat is, the URL’s for your wordpress site, will always include the name of the sub-directory it’s installed in.