I just watched a YouTube video with a AMD RX 460 running GTA at above 90 fps on normal settings. So what is the cheapest card you could get away playing GTA V at on say, 1080p.
For that particular game a 1050 or RX460 or better. The trouble with going for the cheapest though is you have no headroom for more demanding games so every time something more demanding is released you either upgrade, lower your settings, or just can't play it so if you can stretch to a 1050Ti or 1060 or even better it can pay off in the long run.
Another option if you can get a good deal and don't mind some risk is to go second hand. A 970 is still a great choice that will game better than a 1050Ti and should be cheaper than a 1060 for example but just be aware of power requirements - the 1050 & 1050Ti are both very efficient cards that don't use much power.
1080p? Basically a 1050 Ti and up. 1060 6gb will run it very well, a 1050Ti will run it at 1080p, maybe normal settings, and a 1050 might be bare minimum. For your CPU the 1050 Ti seems to be the best choice, but a 1060 3/6gb will work just as well.
GTX 1050 ti for around $150. You should get 60-70 fps at high/very high settings depending on what you select. You might be able to find a used 970 on ebay for around the same price.
For that particular game a 1050 or RX460 or better. The trouble with going for the cheapest though is you have no headroom for more demanding games so every time something more demanding is released you either upgrade, lower your settings, or just can't play it so if you can stretch to a 1050Ti or 1060 or even better it can pay off in the long run.
Another option if you can get a good deal and don't mind some risk is to go second hand. A 970 is still a great choice that will game better than a 1050Ti and should be cheaper than a 1060 for example but just be aware of power requirements - the 1050 & 1050Ti are both very efficient cards that don't use much power.