When it comes to network security, your firewall is one of your most important tools. It is generally a good idea to have multiple lines of defense, such as a router-level firewall and also a server-level firewall that is software-based. Usually, you can block most ports with your firewall, and only allow the ports you need for server functionality to remain open.
The Linux kernel includes a firewall system that is accessible through iptables. The kernel-based firewall is known to be secure but also somewhat cumbersome to manage without other tools. You may benefit from using a third-party firewall tool like APF.
For more advanced network security, you can use a vulnerability scanner that will detect weak points in your server. These tools often do more than network scans, also checking your logs, operating system, and even applications.