So: HDMI and DisplayPort can't do 4k@60Hz without hacks.

HDMI 2 is OK, but there are no video cards that do HDMI 2.

DisplayPort 1.3 is also OK, but there are no monitors or video cards that use it.

DisplayPort 1.2 can do 4k by pretending the monitor is two 1920x2160 monitors and using two DisplayPort streams. How this interacts with your video card depends on how many hacks your driver vendor has implemented. Linux with XRandr treats one monitor as two, leading to much frustration. The Nvidia Linux driver has a bug where if you turn on Xinerama, it breaks both Xrandr and Xinerama, leaving you with one big monitor, which is nice. The Nvidia driver on Windows works correctly by special-casing known 4k monitors. ChromeOS does not do any hacks, and so you get two screens, and windows can't span screens, making it unusable. (It also doesn't ship with HiDPI assets on most platforms, so if you were hoping to run at 2x, some icons are ugly. I have a bug open for this, though.)

HDMI 1.4 can do half of 4k, so if your monitor supports two HDMI inputs, one for each half of the screen, a computer can drive it that way. I did that for a while and it works fine; video cards have long been able to sync vblank between multiple monitors, so there are no weird artifacts. Obviously the same driver hacks must exist to convince the OS that two "monitors" are actually one.

If you were hoping to just plug in the monitor and have it work, too bad. (You may also have to deal with your BIOS not detecting the monitor, and then the machine not booting as a result!)

That said, if you're happy with 30Hz, which is usable but introduces noticeable keyboard latency, 4k works fine with current versions of HDMI and DisplayPort, so you should get a plug-and-play experience. This is especially acceptable if you're just going to play back video, which is all 23.976, 25, or 30Hz anyway. (But there is almost no 4k content available, so just get an HDTV and use the $5000 you saved to crowd-fund some 4k content.)

Now that you have a signal being supplied to your monitor, you need to get the applications to work correctly. Windows zoom feature is awful, or was when I tested it 6 months ago. Avoid. Linux has nothing. Chrome OS has 2x support (at least as of very recent dev channel releases on Panther, the Asus Chromebox), which works quite nicely. Many applications can be zoomed to good effect, like terminal emulators and Chrome. (If you set Chrome to higher than 100% it fetches the "2x" assets from the webserver and displays them correctly; Google Maps looks especially nice at 200% zoom, but so does any site designed by someone with a retina Mac.)

As for hardware... I have the Asus PQ321. It's fine. It is not retina density, of course. I set Chrome to 150%, bump up the fonts in my terminal and Emacs, and leave everything else at the normal settings. Some things are too small, but not unusably so.

4k is not dense enough to turn off font anti-aliasing for most reasonable screen sizes. What we really want is 8k.

While you're waiting for 8k, I'd just save yourself the money and stress and buy a 30" monitor. Every OS handles those perfectly, and the pixels are still pretty small. I have an HP ZR30w monitor; it's nice. The Asus PQ321 is also nice, of course, but are 1.5 extra inches worth the driver pain and $2000?