The inexepensive TV I chose will only run at 30Hz at its native 3840x2160 resolution; more expensive sets will run at 60Hz. However, that 30Hz is also the highest level at which the 13" Retina MacBook Pro will drive a 4K display, so I wouldn't do any better with a more expensive monitor. (The Mac Pro and 15" Retina MacBook Pro can run certain DisplayPort 4K displays at 60Hz, via multi-stream transport.)
While a 30Hz refresh rate is fine for mostly-static images (like windows and text and photos), it's not ideal for video; fast-action videos (and video games) will exhibit some ghosting/shadowing. Some people find these issues more distracting than do others; for me, they're notable enough that I wouldn't plan on watching a feature-length movie at the 4K resolution setting, though I had no trouble with shorter YouTube clips.
Putting it to use
So how does one use a massive 39-inch TV as a display? In my case, I've put it at the back edge of my desk, about three feet from my eyeballs. It works well at that distance, though if I had a different office layout, I'd consider wall mounting it to move it back a bit further, and allow up/down angle adjustments. I put my Retina MacBook Pro on the desk in front of the massive screen, and it's small enough that its screen doesn't visually intrude on my view.
As for how I'm actually using it on a daily basis...I can tell you it's not as seen in this screenshot.
Instead, this is simply to demonstrate what's possible in that number of pixels: six 1024x768 browser windows, a BBEdit document window, a Finder window, and then Mail, Maps, and Calendar along the bottom of the screen. That's an incredible amount of information on one display.
So that's the theoretical; what about the actual? In my day-to-day work, email is critically important to me (as it's our customers' primary method of interaction). As such, I've devoted the left third of the screen to a huge Mail window (in OS X's Classic view). This lets me see about 35 one-line summary emails, along with a preview pane that's large enough even for truly epic-length messages.
To the right, I keep my "accessory" apps, such as my Twitter client, Messages, a small BusyCal window, and some floating widgets (which I float above all via this ancient Mac OS X Hints tip). When I need to edit a graphic, or work in Excel or Pages or some other "big" app, I'll open it in this section on the big display, sizing it as needed for the project--if I need the pixels, I'll cover Mail and everything else, but generally, I try to keep Mail visible at all times.
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