The very first first step on securing a server is installing a firewall (atleast IP tables based) to close all unused or unwanted ports. Once the firewall is installed it is often considered 50% of work done. You can install CSF firewall or APF firewall. Often BFD (brute force detection) utilities comes with firewall.
We will install CSF (Config security firewall) as it is easy to install with plenty of features and easily integrated to CPanel (if you are running)
wget http://www.configserver.com/free/csf.tgz
tar zxf csf.tar.gz
sh /csf/install.sh
Follow the installer and once installed, you can start the firewall.
PHP Code:
csf -s// start the firewall
csf -r
// restart the firewall
csf -f
// flush the rules or stop the firewall.