What are a couple ways to move my site to your server easily?
From your home directory type:
tar -cvf mysite.tar public_html/
then when it is finished, type:
gzip mysite.tar
then download the mysite.tar.gz file.

Upload it to our server into the root directory and type
tar -zxvf mysite.tar.gz

If the directory structure inside public_html is the same it *should* work. It's also a good idea to create the account on our server with the same username as the old server. If the other server is a CPanel based server just create the account on ours with the same username and download the /home backup file on the old server through CPanel and "restore" the backup on our server.