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Gentoo or LFS?
(programming.dev)
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Linux is a family of open source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991 by Linus Torvalds. Linux is typically packaged in a Linux distribution (or distro for short).
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You shouldn’t do either.
You’re setting up a server and a gaming computer. Arch is about as out in the weeds as I would go to accomplish those goals. Both applications are focused on stability and reliability and compiling from source for lfs has a bunch of hidden gotchas that make doing anything a hassle. Not compiling from source also ends up causing you a pile of heartache when the binary you get doesn’t include support for a library you’re using or the version is incompatible or any number of other screw ups that can happen.
If you have a spare computer and just wanna see if you can do it or learn how it works then lfs is the way to go but if you actually want to provide some service or game then don’t switch.