What better place to start than with the operating system? I would love to start with the hardware, but, as I briefly mentioned in my first post, open hardware is still expensive and my church can't afford it; hopefully this will begin to change as open hardware becomes more widespread.
I think it is fairly obvious that both Windows and MacOS/OSX are off the table here; both are closed source and expensive while Windows (at least as of 10, if not before) is entirely too eager to send all kinds of data back to Microsoft that Microsoft has no business having. That leaves a whole host of other OSes. However, since I am pragmatic as well as principled, my choices fall essentially to one of the BSDs or a GNU/Linux distro since GNU/Linux and the BSDs are moderately popular and therefore have decent hardware support.
My experience with any BSD is exactly zero (something I intend to remedy soon) and GNU/Linux generally has better support, both commercially (as in drivers are often available for GNU/Linux but less often for BSDs) and from the community so the BSDs are out.
That leaves the choice of which distro. Unfortunately, our audio booth computer was built before AMD had fixed the mess that was it's GNU/Linux graphics drivers so we purchased a lower end nVidia GPU. Which it turns out doesn't work well with the Nouveau driver; the fan runs at full throttle anytime the computer is powered on. This makes it very noisy and, since the purpose of the audio/visual team is to make it easier for people to hear the service, the proprietary driver has to be used. This eliminates FSF endorsed distros.
Since I am most familiar with Ubuntu based distros (I started using GNU/Linux with Ubuntu and am now on Kubuntu for my personal machine) I chose Ubuntu for the audio/video computer. I initially installed 15.10 on the system and upgraded it to 16.04 LTS once it was available; I have not upgraded it further since it is stable, later versions of Ubuntu have not added any needed features, and leaving the LTS version means I would have to upgrade the OS every 9 months. I will have to revisit distro choice in the future as, since 17.10, Ubuntu dropped Unity in favor of GNOME 3 (and, apparently unlike the GNOME 3 UI team, we have a widescreen monitor where huge header bars and fat buttons waste large amounts of space) but I will cover that when the time comes.
I realize that Canonical/Ubuntu may appear to be an odd choice for someone who claims to be privacy conscious. However, while Ubuntu may be less than optimal "out-of-the-box," the problematic things are easily turned off/adjusted. Additionally, as of 16.04, the most problematic feature has been disabled by default. Apparently, likely emboldened by the success of the horrifically invasive "features" that are baked into Windows 10, Canonical is adding a new data collector in the 18.04 installer that is opt-out. I am still on the fence on how concerned to be about this; I am opposed to it in principle, but it does appear to be a single, easily found button to turn it all off.