Distros that don’t respect your privacy are hard to find, so privacy isn’t really a factor here. You’re just going to get everyone’s favourite distro here, regardless of whether it fits your other requirements.

What kind of hardware do you use?
How stable or fresh would you like your distro to be?
What wind of desktop experience do you prefer?

Also note that the apps you use (on your PC or in the browser) usually far outshadow the OS w.r.t. privacy intrusion.

Open source software usually doesn’t do any kind of tracking or telemetry. Sometimes it is there but then it’s usually opt-in (off by default unless you change it). Most Linux distros contain a huge amount of open source software. So all the code is in the open (which means usually no shady things going on, because a lot of eyes are looking at that code) and there’s often not even an incentive for the developers to gain money directly from the users, except through donations. So if you really like some open source project, please do contribute or donate to it.

So in the end it doesn’t really matter which distro, they all will be MASSIVELY more privacy friendly than any closed source OS like Windows, OSX iOS, or proprietary Android, although to maximize your “chances” so to speak you can go for a purely community-run distro not backed by any company (Ubuntu is backed by Canonical, Fedora is backed by Red Hat, OpenSuSE is backed by SuSE, these are the three big distros with a commercial background. I’m not saying they do violate your privacy currently, but they at least have a greater tendency to do so, because data gathered can be sold, so it might be a business incentive for them. Ubuntu sent users’ search queries to Amazon in the past to gain some more money, but the community outrage caused them to remove this anti-feature afterwards again. Fedora is currently proposing to introduce opt-out (on-by-default) telemetry, it’s not decided yet, but it’s a bit worrying still. So you see, such distros might not be the best choice for “maximum” privacy. But compared to Windows or OSX they’re still magnitutes of miles ahead.

For community-run distros, you can check out e.g. Debian or Arch Linux, or any distro based upon them. For Debian specifially, I recommend running its “testing” branch, because it’s more up to date. Don’t worry about the label - it’s still rock solid stable, because Debian has very rigid testing requirements. They test more and longer than probably any other distro, which means Debian “stable” is very well tested, but also quite outdated. To alleviate that a bit, you can use the “testing” branch. You could even use the “unstable” branch for even more up to date packages, but there’s at least a chance that you get some package dependency problems every once in a while or so, so not recommended for a beginner. Debian is also quite easy to get into nowadays, though maybe not as easy as some of the Ubuntu-based distros. Linux Mint (normally Ubuntu-based) also has a Debian-based edition these days, and Linux Mint is a great distro for beginners. Arch is hard to get into but great for modern desktop usage or gaming because it’s always super up to date. You can also check out EndeavourOS, an Arch-based clone with easier installation. Or just use any distro, really, it’s not that big of a deal currently. They all behave quite well. Mint, Kubuntu or Fedora are good starting points for beginners.

If you have to use a public computer temporarily, there’s really only one choice for a private usage in that scenario: Tails. Put it on a USB stick and use it whenever you’re on an “unsafe” computer. Tails ensures that ALL traffic will be routed through Tor so no one on the local network (or the web, for that matter) can sniff out your data transfers, among other things it does to enable anonymous computer usage (e.g. it leaves behind no logs, doesn’t save any info about your previous sessions, and so on).

Potentially a somewhat unsatisfying response, but it doesn’t really matter.

Most Linux distros are similarly excellent when it comes to privacy and similarly not-necessarily-excellent for gaming.
Obviously, they do have their nuances, but you’ll only start caring about that, as you understand more of the details.

What’s kind of more important, is the choice of desktop environment. It determines the look and feel of the whole OS.
Distros generally come with a default desktop environment, so your choice of desktop may ultimately play into that.

You can just look at a few videos to determine what desktop environment you like. Popular desktop environments (along with a reasonable distro shipping them):

• KDE: very feature-rich, very customizable, rather Windows-like out of the box (Distro: Kubuntu)
• Cinnamon: reasonably feature-rich, reasonably customizable, quite Windows-like (Distro: Linux Mint)
• GNOME: rather feature-rich, not as customizable, more macOS-like (Distro: Ubuntu)

Any distro is good for privacy. Try out OpenSuse Leap or MX Linux with KDE to get a windows-like experience

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Beginner-friendly would be Fedora or Ubuntu.

Then check out Surveillance Self-Defense at EFF (https://ssd.eff.org/) to learn more about privacy

Pretty much all of them, as they’re almost all open source and use similar components (drivers, kernel, userspace). I’d recommend Fedora or Debian just because they are relatively easy to set up, but check out other options on https://distrowatch.com/