CPU would be a limiting factor, but it wouldn't cause choppy gameplay. 1050ti or a 1060 3gb card should be pretty affordable. I think your biggest limiting factor is gonna be if you have the original hdd with that rig, probably pretty slow, and that would be what I'd espect to make things choppy if anything.
I have an i7 2600 and a 970 GTX, plays games fine as long as I stay at 1080p and dont try to max the settings out on games like Witcher 3
Bookmarks