To state the obvious: my personal preference is to run Debian GNU/Linux. My current workplace is a CentOS shop and usually I'm the first to claim that it doesn't matter at all, and distribution specific implementation details are irrelevant for what we do (running a JVM).
Raspbian is often considered to be the *default* distro for the Raspberry Pi (though of course the Pi has no true default as it's just hardware..). Raspbian is based on Debian, optimized for the ARM chipset and small memory of the Raspberry Pi. The Raspbian 2016-02-03 milestone update is the latest release and according to Rapsbian developer Simon Long, "For most people, this is primarily updates and bug fixes to the existing Jessie image ."
The Lightweight Portable Security (LPS) distribution is intended to be used as a live CD to help users remain private. While the idea of a privacy focused distro is not unique (think Tails), LPS is developed by the U.S. Department of Defense.