To be fair, Fedora has opt-in telemetry. It's 100% anonymized, though, and helps with development. I always say yes when I'm running a beta (like now).
That having been said, you should always check the privacy policies of any given distro. They tend to all be pretty up front about it (kinda hard to lie about it when anyone can check your source code...).
AFAIK, though, neither Mint nor Elementary collect telemetry by default, although they might have opt-in like Fedora. Both are based on Ubuntu LTS, but they also both scrape out so much stuff that they're devoid of most of the Canonical junk.
I don't want to be rude, but recommending Arch to a newbie who wants to dip their toe in is just mean. Why not tell them to set up an OpenBSD desktop while they're at it.
And the laptop they're using is from 2015. Why would you need the latest drivers for that?