Although running a web server may make a machine a more attractive target for attackers, it is unlikely to make it significantly easier to break into. There is no point in securing the web function if the rest of the machine offers open doors to intruders. Extra services will, in any case, affect the machine's performance as a web server as well as providing possible routes for break-ins. Keep the system up to date. New vulnerabilities are discovered every week, and are exploited soon afterwards.
Check log files for warning signs.
Each of these should continue throughout the life of the server. Although this requires effort, the procedures are well known. Few people have the ability to discover and exploit new vulnerabilities so the vast majority of security breaches result from well-known problems that could have been avoided. Prevention may seem expensive until you consider the alternative cost of repairing the damage after a breach has occurred. Loss of service generally happens either by accident or through hostile intent, and is usually caused by overloading the server with requests.