Security settings for Linux

Update apache etc to latest versions
(Use the tools that come with your version of linux for this ie yum/apt/etc)

Only allow secure login ie ssh and sftp, not telnet or ftp
(disable unnecessary non-secure services)

Move the secure shell from the default port of 22 to 24
(eg http://www.liquidweb.com/kb/changing-the-ssh-port/)

Put in place a strong password policy - no simple passwords allowed on the system
(eg http://www.itworld.com/endpoint-security/275056/how-enforce-password-complexity-linux)

Don't allow remote root login. Login to root only allowed from the local terminal.
(eg http://www.howtogeek.com/howto/linux/security-tip-disable-root-ssh-login-on-linux/)

Enable Security enhanced linux
(eg https://access.redhat.com/documentation/en-US/Red_Hat_Enterprise_Linux/6/html/Security-Enhanced_Linux/sect-Security-Enhanced_Linux-Working_with_SELinux-Enabling_and_Disabling_SELinux.html)

Check the logs for evidence of problems/hacking e.g.

$ sudo cat /var/log/secure)

Check 'top' every so often to see whether there are unknown users or unknown processes on the system; command:

$ top

Note that many of these actions would need to be checked with (or actioned by) the software vendor to ensure they do not disrupt the operation of the installed software