Go for that 2011 machine! That will be modern current gen experience. It runs up to the latest OSX 10.15 Catalina. I recommend installing 10.13.6 High Sierra though for max compatibility with all 3rd party apps. Up to you though. I think all the usual suspects for media players are up to speed with 10.15.I looked into this unit a bit more. Using the serial number I was able to confirm the following on this Mac Mini I was looking to use as a media player. Mac Mini Mid 2011. 2.5Ghz i5 cpu, 8GB memory, AMD Radeon HD 6630M 256MB graphics, Max OS X Lion 10.7.5.
Maybe I can find install Linux on this hardware? Or maybe I can see if Parallels (Windows) will run on it. Anyway, this is becoming a fun project.
That machine has 2x 2.5" drive bays and supports up to 16GB ram. 8GB ram is more than you'll ever use for home theater though.
PS. If someone is trying to tell you that machine only supports 10.7, they're misinformed or trying to up-sell you.
PPS. You can install any OS you please on one of those. OSX 'just works' the most and requires the least DIY tech.