That sounds like an early C2D Mac Mini from 2007.
It would still run home theater just fine. 10.7.5 should also be fine.
The Apple grifter shop... er I mean App Store said that? Not surprising nowadays...
I never like downloading from the App Store if I can help it. Just avoid the clumsiness of that and download apps as you please form their source as you do online.
This recent trend of gaslighting in the computer arena is ridiculous. Writing software now that shuts you down and tells you to go out and buy new? That's real special...
The 2010 C2D Mac Mini will run at least up to 10.13.6 FYI.
I still recommend the 2011 or 2012 machines if you're going out to snipe for one.
But if you already have that 2007 kicking around, scare up a SSD for it and it will do a bunch.
There's lots of capable hardware available. I liked the Jobs era Macs. Right now you can often snipe them used for less than a new machine with half the spec. The 11s and 12s are still high end current spec relevant. OSX has always just worked for the most part and was the only choice for the pro audio stuff. Still just works but Apple is trying to break it and they're starting to blacklist many of the fully compatible Jobs era machines with the new installers. Turning into Microsoft in other words. Linux is looking like the future. Pro audio and video is already starting to switch gears that direction.