Not a perfect answer, but probably the two most important things will be the php version, which should be version 5.2.xx or higher, and the php.ini memory limit which should be 32MB (64MB optimally). Also, cURL enabled to run certain extensions.
suPHP permissions errors usually refer to the file and directory permissions. To tighten security, this setup does not allow anything to be "globally writable" so directory permissions of 777 and file permissions of 666 will not work.
All Joomla stuff should run fine if you set all directories to 755 and files to 644. You can set your configuration file and your htaccess file to 444 for a little better security.