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It’s a little hard to decipher what you mean. I think I understood that you basically want to have a headless gaming rig so you can stream your games in the rest of your network. The closest you would get is probably Bazzite, and configure it to directly boot into steam big picture mode so you can use steam link on your connecting devices. If you would like a platform agnostic setup you could look into sunshine. That will involve more tinkering tho.

Maybe Bazzite because it’s geared towards working well with gaming out of the box.

I’d recommend CachyOS if you’re trying to squeeze the best gaming performance out of the hardware

Even “heavy” linux distros are easy to run for a pc capable of running and streaming modern games. Lightweight distros are mostly relevant for older or underpowered hardware.

Linux uses less resources than windows by default, any is better performance and lighter, cachyos might be easier to tinker with, I got sunshine working on it fairly easy.

You mean as a file server? I’d probably use a minimal Debian installation. But almost any distro should have a minimal flavour.

should be fairly simple with any distro. personally, id recommend mint or something for ease of use. install steam, and you can use steam link for android (chromecast, roku, firestick, mobile), or steam link for linux (raspberry pi etc). steam has built in compatibility for windows games running on linux, and a built in streaming setup. a bit of an all-in-one solution.

you can try a steamdeck-like distro as others have suggested, but they may be less easy to learn on if youre not too familiar with linux already.

keep in mind nvidia drivers are a sore spot in linux, so if possible try to use an amd graphics card.