If you're planning to use that rig just for watching movies, playing some games here and there casually, the 1050ti is more than enough. If you'll use that machine as your main gaming rig, go with a 1060 6GB for 1080p, for resolutions higher than that you'll need a 1070 and 16 Gb to be futureproof.
BTW, I have a 1050ti in my HTPC and Tekken 7 run flawlessly at 1080p and 60 fps. That card can handle any fighting game at that resolution.