Ideally, one would just have a 4K 60Hz TV that has DisplayPort in if it is intended to be used with a computer.
Ideally....but there are very few (Panasonic; a couple others?) because HDCP, and of those...Most of them either aren't great (edge-lit/inferior innolux panels) or are incredibly expensive. Yes, I know there are plans to incorporate HDMI2.0/HDCP2.2 into DP, but we haven't really seen that yet.
I settled on (pretty much) the first affordable 4k tv with HDMI 2.0 (IOW 4k60 capable). It works fine (I bought it and 970 within a week of their launch), granted beyond 24hz is YYCCYCBBRBRBRBYBR (okay, maybe just YCYBR 4:4:4) instead of RGB (because initial implementation of HDMI 2.0 sucked; there was pretty much only one scaler available), but it still looks good-enough considering the drawbacks versus benefits. Most media uses the 4:2:0 YUV anyway, so there really isn't any color loss, and pc gaming/desktop use at 4k is worth the slightly different color space...even if the only thing that a 970 can accomplish high quality 4k60 is something like Dark Souls.

. There's also no rule against natively feeding a 1080p signal (which this tv is supposed to support at 120hz...but sometimes results in momentary occassional signal loss...that they are supposedly fixing at some point) and upscaling it to 4k. I often do this (1080p60 upscaled/dithered) so I can play games at high quality...still looks decent.
One thing I find incredibly helpful is things like MADVR/MPC-HC supporting switching refresh rates depending how how the media was encoded (23/24/25/29.97/30/etc), which my tv supports. I imagine those using monitors often use this as well (if not reclock), as it eliminates judder (and allows one to increase quality at the lower frame rate). I find this a much better experience than trying to force interpolation or pulldown, as good scaling + good interpolation is WAYYY too stressful on current cards, and of course that built into the tv itself causes lag and the quality suuuuccckkkks (I force everything through the GPU; there is a 'low latency' mode in the tv with no perceivable lag and the added benefit of having no tv picture enhancements enabled).
It's another one of those reasons I look forward to the next-gen (14/16nm) gpus and cpus. Beyond better media engines (for hopefully high-quality HEVC/VP9 decoding/scaling), they should *hopefully* have enough fp16, if not fp32, to be able to massively improve image quality through (opencl etc) upscaling/interpolation. I certainly wouldn't mind 48-59.94/60fps interpolated media if I could run SVP at high quality. As it sits, on my overclocked 970 anyway...It can only do so much.
If you can get 4k30 working, which should be easy enough on most sets, I think it will be fine for media, Just make sure you try to set it up (ala the things I mentioned; switching refresh rates to that which media is encoded, cranking up MADVR settings as far as you can) carefully if you want a good experience.