A new or used mini PC is good enough. No need to build. 16GB ram mini pc is recommended though for the future.
https://www.amazon.com/GMKtec-Windows-Computer-Business-G3/dp/B0CQ4XQ2WG
I personally owned a 32GB 5700U mini pc from GMKtec, very satisfied. New model has been updated to 5825U, same price
https://www.amazon.com/GMKtec-Mini-PC-Ryzen7-5700U/dp/B0CD7Y4C5Y
Add a small screen if needed.
https://www.amazon.com/MNN-Portable-15-6inch-Ultra-Slim-Speakers/dp/B0B9NNWXVP
Lantis3...
I like your first link, that GMKtec Mini PC. Just need HDMI out and a USB or two for wireless logitech and a flash drive. Best part is, I don't even need the monitor you linked if I can get it working with my projector. It's got wifi and windows 11.
from description:
【4K Dual Screen Display】Mini desktop computer is equipped with Intel UHD Graphics(max 750MHz), supports 4K video playback and AV1 decoding, connect the pc with a projector as a home theatre, enjoy a variety of entertainments. Two HDMI 2.0 ports allows you to multi-task efficiently on two 4K@60Hz displays.
All for $127.99.
Your second link, at $330 seems more than I need, but I could spend more than $128 if there's a good reason to.
The $128 comes with 8GB DDR4+256GB N100, but there's an upgraded version for $144.49 which buffs me to 12GB DDR5+256GB N97.
I mostly build highest end gaming desktop PCs, so I never have to think about processing speed when doing simple desktop tasks, streaming, moving files, etc. Am I going to have any of those issues with a PC this cheap?
I appreciate you saying you had good luck with the other GMKtec. I know nothing about this brand. Can you or anyone else tell me more about it, perhaps based on the hardware?
Anyone have any reason to doubt this PC for my needs? Anyone have something similar?
Really apprecaiting this feedback. Good finds.
*Bonus question. My wife likes to play the Sims 4. Would this run that just fine?