As I posted on another thread, I was debating whether to keep or sell my late 2012 2.3 GHZ i7 Mac mini, as I also have a 2015 13" MBP. I decided to keep it. A couple weeks ago, I bought a 28" Samsung UE510 4K monitor at Costco for $300. I read various conflicting posts about the monitor's specs, and the best I could determine is that Samsung has upgraded the specs over the past couple years. In any case, while it isn't the best 4K monitor available, for $300, it's a bargain. It works great with my MBP, and also with my HP EliteBook running Windows 10, which is the computer I use for my job. (I'm quite happy with Windows 10, but that's for another thread.)
Naturally, I wanted to see how the monitor works with my Mac mini. I bought an inexpensive Thunderbolt-to-DisplayPort adapter on Amazon that received high ratings. My verdict is that the mini looks a bit soft at all resolutions, but it's not unusable. Once you get used to Retina or true 4K, anything else has the "screen door" effect. At 2560 x 1440, the monitor looks a bit soft, but whether that softness is better or worse than the "screen door" effect with a native 2560 x 1440 monitor is a matter of opinion. I tried the demo version of SwitchResX and set the monitor to 3840 x 2160 at 30 Hz, and it had the same amount of softness.
1080P using the mini's HDMI port is terrible with the Samsung monitor.
For now, I'm using the mini with a native 1080P monitor, which I've been okay with for the past several years. I might get a native 2560 x 1440 monitor; there's a Lenovo monitor I've seen on sale for about $150. But my recommendation is that it isn't worth bothering with 4K for late 2012 Mac mini.
Naturally, I wanted to see how the monitor works with my Mac mini. I bought an inexpensive Thunderbolt-to-DisplayPort adapter on Amazon that received high ratings. My verdict is that the mini looks a bit soft at all resolutions, but it's not unusable. Once you get used to Retina or true 4K, anything else has the "screen door" effect. At 2560 x 1440, the monitor looks a bit soft, but whether that softness is better or worse than the "screen door" effect with a native 2560 x 1440 monitor is a matter of opinion. I tried the demo version of SwitchResX and set the monitor to 3840 x 2160 at 30 Hz, and it had the same amount of softness.
1080P using the mini's HDMI port is terrible with the Samsung monitor.
For now, I'm using the mini with a native 1080P monitor, which I've been okay with for the past several years. I might get a native 2560 x 1440 monitor; there's a Lenovo monitor I've seen on sale for about $150. But my recommendation is that it isn't worth bothering with 4K for late 2012 Mac mini.