Upgrading my Scrapyard Wars inspired computer for streaming

[VIXERXYZ]

Budget (including currency): ?$?$?$?$

Country: USA

Games, programs or workloads that it will be used for: OBS, variety of AAA and retro games for streaming to twitch

Other details (existing parts lists, whether any peripherals are needed, what you're upgrading from, when you're going to buy, what resolution and refresh rate you want to play at, etc): 

I have an AMD FX-8350 with 8gb 1866 mhz ram (single channel) on a gigabyte 970 board, I use a 512gb ssd and a 500gb hdd for storage in my machine. I am looking to stream games and possibly just a 1080p talking stream, not looking to do higher than 1080p currently. I have a 500w psu and my cpu is currently clocked at 4.3 ghz. Now for the most s part of my build, the gpu, I have a radeon 5850 and it is definitely showing its age. Although it has handled an insane amount of games for just how old this mid tier card is I desperately need to upgrade. I built this system just before the pandemic for $195 and I am looking for recommendations for what is going to pair the best with the rest of the hardware I have. I am not looking for a particular budget because I am most likely going to be taking this to the second hand market as this is a Scrapyard Wars inspired build at the core and I would like to keep it going. The psu is 80w gold and was brand new just so no one is concerned about the stability of that. 

Thank you all!!

[resolve_beta]

it is very odd that you can stream on 8 gigs of 1866mhz but, the card i would recomend is 1050 ti for 100$ or less.

[VIXERXYZ]

Well I do plan on upgrading the ram to at minimum a 16gb kit of 2400 ddr3. I also didn't say I can stream but I am looking too. I am having quite an issue with dropping frames. I did used to stream on a very similar setup but that was when the 8350 was a brand new chip and I was running it with a 480ti. but the card isn’t the only component I want or am willing to change I just don’t  want to have to change cpu or board at least right now I would like to leave those as well as the 500w psu that is why i mention the clock speed of the cpu because it is slightly overclocked and I do plan on going higher that was just my first increase but it was stable so I didn't continue to push the system. I should also mention that this system doesn't have to perform competitively. The plan is to have my wife stream playing games and working with the xbox adaptive controller to try to make the best experience in gaming for someone who is a quadriplegic.