For a long time, I’ve just put on DejaVu fonts and been done with it. Generally good enough Unicode coverage for me. But I know it’s been years since DejaVu’s been updated, and I wonder what’s very common today.
[As for the terminal, I’m guessing it’s usually still the standard fixed Unicode fonts?]
I don't think it's that common, but if you're looking for good fonts, I really like IBM Plex Sans/Serif/Mono. Has good Unicode coverage as well and is "open source" (or whatever it's called for fonts).
I use these too, and Fira Code and Hack for coding.