You've got some good suggestions already. Here are a couple that I think are good for somebody that is fairly new to the deep rabbit hole of anime tropes/conventions:
Mushishi - My personal favorite anime of all time. Very contemplative and melancholy. Don't binge this, just watch an episode before bed or something like that, and let it sit in your brain.
Frieren: Beyond Journey's End - This just recently finished airing its first season and was excellent in every respect. Classic high fantasy story (think Lord of the Rings) which follows the near-immortal elf Frieren in her travels. Very approachable for previously non-anime watchers.
Cowboy Bebop - An all-time classic space western following some bounty hunters.
One Punch Man - A humorous take on the superhero genre. If you are looking for something more comedy oriented, this is a decent starting point.
The problem with recommending opm as a starter is that it parodies a bunch of shows and Manga that OP probably won't have the references for. I would worry that OP might miss most if not all of the jokes without the context.
They don't "need" to know the stuff they are parodying, true, but it's a lot less funny without that frame of reference. It's like listening to a Wierd Al song without knowledge of the original.
Oh no, he might not understand that Saitama's shirt says boobs? How will he ever enjoy the show?? I watched OPM as one of my first anime, got almost no references and its one of my favorite anime of all time.
No one disagrees. Our point was that someone enjoys a parody more when they have a frame of reference of what is parodied. I mean it’s the whole point of a parody. One can enjoy OPM but if the same person had seen 500 battle shounen up to the point where they’re fed up with the same tropes, OPM is just a million times funnier than when that is just first anime.
I don’t want to shit on your favorite show here, but it’s just common sense that a parody is better if you know what is parodied.