If you are running 1080p there are card choices for you to play overwatch near max settings with a GPU around $100.
I recommend you continue saving to at least get an AMD RX 480 for about $200 dollars and that will play EPIC settings which is maxed settings.
But lets say you couldn't spend any more than $150, then I would recommend GTX 950. Here is one on amazon for less than $150 - MSI GTX 950 $132.99.
But lets say you couldn't spend any more than $125, then I would recommend a, like the others an GTX 660ti.
But overall, it seems like the GTX 950 is my overall recommended card in your case.
Edited: after seeing your using a intel i5, you should be fine to hit higher frames these cards are intended to hit. If you can't hit the desired frames, then you might want to look into safety overclocking your CPU and GPU.
The NVIDIA GTX 1060 just came out for MSRP $250, that and the AMD RX 480, destroys current 1080p games! IMPORTANT: in order to get any of these new cards listed for their MSRP, you will have to wait for less demand and more supply. Cause right now people are buying these cards for more than what they're supposed to cost. Or buy them from a BestBuy or something. Usually, BestBuy doesn't push their prices up based on supply and demand.
As for windows G, im not sure what that is, but i know people who use twitch that stream with twitch has that equal or more powerful cards listed in this post with no problems at all.