Linux, in either desktop or server config, will do.
Generally, server configurations are “more secure” in that they have network services turned off by default, so if this system is going to be exposed to the internet, then you’ll want to start there first. Also, many server configs come with more network services available (SNMP, SMTP, NTP, LDAP, DNS, etc.). (However, these can be easily added to “desktop” configurations, as well through the distributions package management system.)
If you’re new to Linux, you may want to try the latest Fedora Core first, then move on to RHEL if your support requirements demand it.