Hi virtualc08
Check out the Duplicator plugin.
I have used it for a few site migrations. You install the plugin on the old site. You then use the plugin to create a package (a type of backup used by Duplicator).
You can restore this package on another server.
Just FTP the package, and an installer.php file to the new server, create a new empty database and navigate to the installer.php.
Once you get to installer.php you will need the database name that you created, as well as the username and password.
I have even created a package of an 'empty' Wordpress with all of my favourite plugins, a Contact Us page, an About Us page, and a Privacy Policy page. I also have an AdSense plugin installed, and configured with all of my Ad codes. So whenever I start a new AdSense site, I just restore the package, and can start adding content immediately. No time wasted on the normal setup, installing of plugins, permalinks setup, etc.
I haven't tried it with a big site yet, although I have migrated an eCommerce site of mine, and it worked really well.
Let me know if it works for you.