If you are interested in only movies, HD 6570 is enough (supports the highest settings). If you also play videos, HD 7770 is the minimum for the highest settings. (7770 is roughly 1.5 times better than 7750.) Playing SD/HD/FHD contents in 720p/768p/1080p displays, of course.
4K has two meanings:
1. Play SD/HD/FHD contents in a 4K UHD display. Upscaling them with the highest settings (x5.33, x3, x2) is very demanding.
1a. SD/HD/FHD movies: HD 7770 is good for the highest settings.
1b. SD/HD/FHD videos: HD 7970 is necessary for the highest settings. HD 7770 is good for Lanczos3+AR.
2. Play 4K contents in a 4K UHD display. Two points of consideration:
2a. Decoding AVC = H.264 is easy for Pentium IVB (because of Intel Quick Sync). Decoding HEVC = H.265 could be hard. You might want to have a real quad-core processor (i.e. Core i5) for future proof.
2b. If the resolution of the content is identical with that of the display, then only chroma upscaling is necessary, that is easy for a decent GPU. However, if the former is larger than the latter (e.g. 4096 × 2304 > 3840x2160), then downscaling is necessary and the highest Catmull-Rom+AR+LL is demanding.
So, Core i5 and HD 7970 (best upscaling for movies/videos) or HD 7770 (best upscaling for movies, medium upscaling for videos) are recommended for 4K.
HD 8000 series may not come until 2014 (source
But Fudzilla says, New AMD desktop cards in 2H 2013
. I don't know which is true.