I used a 39" 4k display for a while (before I moved and decided to use it as a "temporary" TV) and it "Just Worked" as I'd expect it to. While it's only 30Hz at 4k, that more than meets the requirements you put forth of word processors, IDEs, etc. It plugs in over HDMI and doesn't require the newer standard or any special cables to use. I ran that display along with a 1440p display off of a single Radeon 7850, which is neither super expensive, nor loud, and for normal use there were no issues to speak of. Games were a little bit iffy at 4k, but 30Hz wasn't great for most of the most power hungry games anyway. I just switched over to the other display.
It was great, I could have a ton of terminals open, a browser, text editor, a video playing and it didn't feel cramped. Essentially having 4 19.5" 1080p monitors without the borders.
Writing this out makes me want to take that back as my main monitor, I guess I'll have to find a TV to replace it.