nVidia drivers for Kepler have for some time done an excellent job compressing 4k60 into the limited bandwidth of HDMI 1.4. It's not perfect--some things like Control Panel elements flicker noticeably so perhaps those are actually being rendered at 4k30, but most things seem fine at 4k60 with only some loss in color accuracy (4:2:0 has only 1/4 the color information of 4:4:4 YCbCr )
That said, Kepler can only hardware decode H.264 in 4k60 which is something even your 3GHz Athlon II could do in software. There's no chance that CPU could software decode H.265 4k though without dropping frames, so I'd suggest a GPU that could fully hardware accelerate that. The oldest one that can is the GTX950, which can also hardware accelerate VP9 as used in 4k Youtube videos. If you don't play >720p games a GT1030 would serve just as well.
Supposedly nVidia finally replaced the GT710 in January with the new GT1010 which is a cut-down GT1030 but I've never seen one for sale. Too bad as that would likely be near MSRP since it's no good for either gaming or mining.