I always recommend installing WordPress manually yourself. Some companies will insert a link crediting the hosting provider for the install. In the past, I’ve experienced 1-click installations that are not running the latest version of WordPress.
In terms of migrating your website, you should follow this guide: http://codex.wordpress.org/Moving_WordPress. Smashing Magazine also provide an easy tutorial: http://wp.smashingmagazine.com/2013/04/08/moving-wordpress-website.
In a nutshell, you’ll download the whole site via an FTP (including the WordPress core files, plugin folders, uploads and your themes) and then transfer these files to the new server. Using something like phpMyAdmin, you’ll need to export the old database, create a new database on the new server and then import the data. You’ll find all the information you need in the links I’ve provided.
Update
In the comments @Dan has suggested this article in the codex for those who wish to move the wp-content directory: http://codex.wordpress.org/Editing_wp-config.php#Moving_wp-content_folder.
@Brijesh This article explains the benefits of moving your wp-content folder and gives you detailed instructions: http://www.paulund.co.uk/move-wp-content-folder-to-different-location.