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What should I buy?
I am currently using NVIDIA GeForce GT 530 [Display adapter]
According to this site: http://www.techspot.com/review/1180-overwatch-benchmarks/page2.html, the best deal (good performances / low price) for your planned use would be the GTX660ti (https://www.amazon.fr/Asus-GTX660TI-DC2O-2GD5-graphique-Geforce-PCI-Express/dp/B009KZ4DK4).
This GPU runs Overwatch, ultra settings, 1080p (I assume that its your resolution) at ~80fps and is around 100€.
However, becarful, you didn't say your current configuration (especially CPU): for a twitch/live record of your screen, I'd say that CPU is as much important as GPU. Besides, the 80fps performance had been get using a i7 6700k wich is quite de best CPU you can get for gaming, for now.
So you should tell us more about your config in an edit and I'll be able to edit this answer accordingly.
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.
Newest Edit The NVIDIA GTX 1060 just came out for MSRP $250, that and the AMD RX 480, destroys current 1080p games! IMPORTANT: in order to get any of these new cards listed for their MSRP, you will have to wait for less demand and more supply. Cause right now people are buying these cards for more than what they're supposed to cost. Or buy them from a BestBuy or something. Usually, BestBuy doesn't push their prices up based on supply and demand.
As for windows G, im not sure what that is, but i know people who use twitch that stream with twitch has that equal or more powerful cards listed in this post with no problems at all.
This is 10$ more than your budget but I don't see why you cant chip 10$ in. This is a very solid card but your wishlist is very extravagant for this price range. This should meet your requirements except high settings and recording is just way out of your budget so you would probably have to play on medium. Or if you want high fps maybe low-medium.
Resources:http://gpuboss.com/gpus/GeForce-GTX-750-Ti-vs-GeForce-GTX-660-Ti
According to that It is equal and slightly better than the 660 ti so if the website the person referenced is true than you should get equal fps or better.
