Works fine in Monterey. The Mac mini 2014 supports up to 2560x1600. In fact, that's what I'm typing on right now - 30" Apple Cinema HD Display. However, my 1920x1200 23" Apple Cinema HD Display also works in Monterey. The Mac mini also supports HDCP if your monitor supports it.
Worked fine with my 1920x1200 23" Apple Cinema display and adapter. That was long before Monterey however.
I don't think there's any problem with 1920x1200 on "newer Macs". The problems are related to the DVI interface and adapters. From what I've read, using the HDMI port with an adapter is more problematic than the USB-C interface.
He's thinking of using the mini-DisplayPort, which will work fine. But actually, HDMI should also work fine.
Come to think of it, with a 2015 MacBook Pro I didn't have a mini-DisplayPort to DVI adapter, so in a pinch I used a mini-DisplayPort to HDMI adapter, and then an HDMI to DVI adapter, and that worked fine at 1920x1200.
If anything, I've had more problems with USB-C.
And yeah, as
@Fishrrman says, don't buy the 1.4 GHz i5 with 4 GB RAM model 2014 Mac mini. They're all over the place. The good news is the 2.6 GHz i5 with 8 GB RAM model 2014 Mac mini is also all over the place. You just need to be careful to read the details when buying used.
Also, you can buy a hard drive model, and then install your own NVMe SSD. You just need to buy the adapters and tools. The actual SSD install is dead simple. Takes a beginner literally less than 10 minutes (not counting installing the OS).