A dedicated server is by all measures a major investment. A good piece of dedicated hardware doesn't come cheap, but the benefits of having an entire server's resources at your disposal completely outweigh the financial considerations. You install the operating system of your choice, you decide how many websites you are going to host on a machine, and you apply available resources exactly as you see fit.
The downside, of course, of a dedicated machine is that you are completely in charge of ensuring its welfare, and in particular, you are in charge of safeguarding the websites a machine hosts. There are of course a number of straightforward maintenance and management issues you need to build into a work routine and work procedures to ensure you safeguard your dedicated server and the treasures it stores.
First, make sure you house your machine is a safe physical location. Physical security of your server is just as important as defending it from the range of cyber threats available the Internet offers.
As far as those cyber threats are concerned, fend them off by using encryption when accessing websites. Using SSH/SCP ensures login details (user names, passwords) are encrypted and unavailable to all but those who permitted to access them. Use port 22 for SSH/SCP and ensure all other ports are completely blocked.
In this busy, busy world there is also always an inclination to "shortcut" on passwords, and people forget they are an essential aspect of your server security. Of course your website name plus '123' is easy to remember, but you don't need sophisticated software to hack a system protected in this way. You just need brute force (an exhaustive key search) - or even just a bit of common sense and a bit of luck. Try this as an alternative:
You can generate solid passwords at websites like Random.org.
Of course, protecting against viruses is bottom line basic stuff as far as servers are concerned, but it is curious how many people just don't do it. Install good antivirus software and ensure that updating antivirus definitions is also built into your procedures. In addition, keep abreast of software updates - ensure that all known vulnerabilities are dealt with using the software company's patches. Some software updates might be optional, so make sure a regular visit to the software company's website is an ongoing and regular part of your workload.
Of course, safeguarding a dedicated server is, in many instances, as straightforward as safeguarding a PC. The only problematic issue is remembering to do it. Make sure quality measures become your norm and build safeguards into your daily procedures. That way you will safely enjoy your dedicated server for as long as you going to use it.