Build Help for Gaming & Streaming Separately

[curlyfry78]

Budget (including currency): $550-650 USD for everything except the case (cpu, gpu, cpu cooler, mobo, ram, ssd, psu)

Country: US

Games, programs or workloads that it will be used for: Playing League of Legends and MapleStory at 1080p and streaming

It should be able to stream to YouTube (1080p60) and Twitch (720p60) concurrently, and the streaming would happen completely separately from the gaming - it would just be of a webcam (or possibly a mirrorless camera/capture card). I don't need the capability to stream and game at the same time.

Other details:

Will be using a 1080p 165hz monitor

Just need a wired internet connection

Prefer the PC to be quiet while streaming

Prefer mATX size

Would like to buy within the next 2-3 weeks

 

Do I need a GPU for this use case? What CPU/GPU would you recommend?
I have an option to get a 9600k, z390, 16gb (2 x 8gb) ddr4 3000 c16 ram, and noctua u12 for $100 - would that be good for this build? Or should I look for something like ryzen on the AM4 platform?
For gaming, would I need to spend more on the graphics card to be able to play at 144 fps? And would 16 gb of ram be enough for this build?

I’m open to buying used components on eBay/Micro Center. If you strongly recommend increasing the budget, please let me know. Any advice, general guidelines, and component suggestions would be appreciated!