Anon's Guide to 4K and Screen Resolution

Disclaimer: this isn't supposed to be a perfect method, but it should be enough for an informed decision. Also, this isn't meant to dissuade you from buying a 4K monitor or TV, but to help you decide whether it makes sense paying a premium for the extra resolution or the extra inches on the diagonal.

Before buying a 4K anything, I suggest you to check what dpi your eye can resolve at your normal viewing distance and then calculate what size the panel should be at 4K resolution to roughly match your sight, and then follow from there.

To do this, print at the highest dpi possible (600dpi should be plenty) this
http://www.takinami.com/yoshihiko/photo/lens_test/USAF.pdf
and be careful to print it using the pdf dimensions and not fit it to the page: it's important to preserve the original dimensions, otherwise the results would be skewed.

Then place it where your screen would be, and go sit wherever you sit when looking at that screen. Also, make it so that the lighting matches your average lighting condition of the room, since visual acuity increases with the amount of light hitting your eye: too much or too little light will skew the results too.

In this page
https://en.wikipedia.org/wiki/1951_USAF_resolution_test_chart
you'll find how to obtain the lp/mm value from the chart.

Then you need to convert from lp/mm to dpi: just double the lp/mm value and multiply it for 25,4.

At this point use this
https://www.omnicalculator.com/other/pixels-per-inch
inputting the 4K resolution, or any resolution you want to check, and the dpi of your vision to calculate what diagonal the screen should have to match your visual acuity. Note that you can also input the width of one line value from the test chart into the dot pitch field of that calculator: they're equivalent.

Usually either the screen would need to be too big, or you should sit closer, so at this point you can play around with the calculator trying other resolutions and other screen sizes of your choice to find what's the best match with your particular case.

Keep also in mind that at close distance your perceived dpi varies dramatically, because every time you halve the distance the perceived dpi almost double, so take those values you calculate with a grain of salt and check with different postures: if for instance you tend to lean towards the screen and also have a reclining chair and often lower the backrest, the small difference in distance between those two position can result in quite dramatic difference in perceived dpi; consider carefully at what distance or interval of distances you commonly watch the screen, and base your evaluation on that.