Quick answer: GTX950 2GB
http://www.amazon.com/EVGA-GeForce-Graphics-Card-02G-P4-2951-KR/dp/B013WQCC8Q
Long answer (sorry so long)->
Recommended GPU (depends on budget):
Update:
A weaker CPU is going to bottleneck the GPU.
Power Supply is important too.
64-bit Windows is a must, 32-bit will not work well at all.
*So please post basic specs... for example:
- Windows 7 64-bit
- 4GB DDR3
- AMD FX-4300
*Again, you do not, nor SHOULD NOT actually set game resolutions to 4K unless you can actually game at max settings whilst maintaining a solid 60FPS.
With a half decent card (GTX960 or better) you should be gaming at either 1920x1080 or 2560x1440. For example, Skyrim with mods I'd use 1920x1080 because frankly the higher resolution only makes the text on your HUD slightly sharper which you won't likely notice when gaming (but at the expense of performance drop).
CIV5, Starcraft 2, Diablo 3 (mostly top-down "god games") should mostly be at 2560x1440, though there are a few games I can crank up to 2560x1440 that are older shooter styles and still get 60FPS on max settings.
So... that said, here's some recommendations and get at least 3GB of VRAM if spending over $200USD though cheaper cards can be had with only 2GB which can give you an excellent experience too:
1) GTX950?
You did say "cheaply" so not sure what that means. This should handle 4K/60Hz desktop and when tweaked to proper settings/resolution a pretty good gaming solution.
It has 75% the processing power (at same frequency) as a GTX960 so you probably can expect 75% to 80% the frame rate for games.
http://arstechnica.com/gadgets/2015/08/review-nvidias-gtx-950-is-a-highly-capable-good-value-gpu-for-1080p-gaming/
http://www.amazon.com/EVGA-GeForce-Graphics-Card-02G-P4-2951-KR/dp/B013WQCC8Q
2) GTX960 4GB (not 2GB)
EVGA, Asus, or MSI are my top choices (see customer feedback scores and comments)
3) GTX970, 980, 980Ti
Nice but progressively more expensive and budget not stated.
4) AMD cards:
R9-380 4GB or better
I have a few issues with AMD but won't bother to go into that here....update: avoid AMD with an older CPU or you'll be even more bottlenecked in DX11 games due to inefficient AMD drivers.
Update: There might be some slightly cheaper cards from AMD that will be "good enough" depending on games you play though be sure they support 4K/60Hz.
BENCHMARKS:
a) R9-380: http://www.kitguru.net/components/graphic-cards/luke-hill/sapphire-r9-380-nitro-4gb-review/11/
b) Most GPU's (average of about 20 games):
https://www.techpowerup.com/reviews/Gigabyte/GTX_960_OC/27.html
Summary:
a) must support 4K at 60Hz via DisplayPort (to get native 4K, otherwise must upscale on monitor)
b) at least 75% performance of GTX960 (see Techpowerup link) recommended
c) I prefer NVidia but don't want to go into too much detail here (DX11 driver support, PhysX, power draw..)
*avoid AMD due to DX11 drivers and older CPU.
d) *Again, game resolutions can and should be set by optimal experience and rarely if ever at 4K.