Is it better to use an HDMI -> DVI cable or a Mini DisplayPort -> DVI cable?
Does it matter as far as quality? The monitor I bought for my wife's "new" 2012 Mac Mini only has VGA and DVI inputs.
The only time it's something to worry about is with a display that takes dual-link DVI (typically, 27-inch or larger). Then, you'll want to go DVI whenever you can for best color. (There's a glitch in the way that the Mac detects the display and sends color information using other connections.)
Apple released a new Mac mini model? I completely missed that news! The current "new" model is 2012.
With new standards for HDMI coming out, I am guessing tools/utilities to change the resolution are going to become popular, maybe even necessary. I was trying to test out 4K TV's with my Win8 laptop and had to use a resolution overlay program to force 3840x2160 over HDMI.