Even if you want to stick with an Open-Source operating system, Linux isn't your only option. There are at least three variants of the BSD (Berkeley Software Distribution) Unix tree - FreeBSD, NetBSD, and OpenBSD. OpenBSD in particular has a strong focus on security that has held up well over many years. They are common enough to have plenty of helpful followers, and being Unix they are at least reasonably familiar to someone experienced with other flavors.
They don't necessarily support all the exotic hardware that Linux does, or some of the more advanced/experimental OS features (SMP support in particular is a bit awkward) but they are nevertheless full-featured and production-ready. In some ways (like their packaging system) they have definite advantages over traditional Linux solutions.