Debian 8 (Jessie) 64bit is the most counseled, deployed, and tested Linux distro, and it's the platform on which most FreeSWITCH development is primarily done. If you're into Linux, and in doubt about which distro to use, definitely use Debian Jessie. All libraries, dependencies, kernel features, and so on are tested each minute for FreeSWITCH usage in every possible configuration, use-case, and work load. Debian (Raspbian) is used on Raspberry Pi too, and the Pi3 has enough horsepower to handle video. Immediate runners up as Linux distros for FreeSWITCH are CentOS/RHEL 7 and Ubuntu 16.04 (Xenial). Please be aware that Ubuntu tends to be a little too much on the bleeding edge, to update packages and libraries often, even in Long Term Support (LTS) versions. We support Ubuntu, we even distribute ready-made packages, but if you don't have a strict company policy, go for Debian. If you come from Ubuntu you'll find yourself completely at home, and on the safe, conservative side. FreeSWITCH 1.8 announcement stated there will be support for Debian 9 "Stretch", that over time will become the preferred Linux distro.
Support for Stretch will probably be backported to FreeSWITCH 1.6, but please check our http://freeswitch.org/confluence official documentation for up to the minute updates.