Who should be the owner of the files?
NOT THE WEBSERVER UID!!!!
The webserver only needs read access to most of the files. There may be updateable files in specific directories depending on how Joomla is configured, but lets not worry about that just now.
Set up a group for the users whom need write access, say webdev. Then (as root):
cd $WEBROOT
find . -type d -exec chmod a+rx,o-w,g+ws {} \;
find . -type f -exec chmod a+r-x,o+r-w,g+ws {} \;
find . -exec chgrp webdev \;
Files are then readable by the webserver via 'other', writeable by the webdev via the 'group' permissions, and new files / directories will be created owned by webdev.
If you need to make specific directories writeable by the webserver uid, then chmod o+w them (and add a .htaccess file / modify the webserver config to prevent direct access by the webserver if they are inside the document root).
And please stop using FTP. It's an accident waiting to happen.