If you have cpanel on your account its better to backup through it.
If you don't and have Shell access then login and pack your files like,
Code:
tar -cvf mybackup.tar public_html/
Backup your sql data through the nuke panel > backup DB.
When you moved, upload the mybackup.tar unpack your files like,
Code:
tar zxvf mybackup.tar
and restore your db with phpmyadmin or any other gui sql tool.