As far as series go: If you need a good time, Miss Kobayashi’s Dragon Maid is a must watch; If you wanna get more serious, an epic space opera is also an important milestone, try Mobile Suit Gundam or Super Dimension Fortress Macross; Once you get used to anime in general, you can also try Natsume’s Book of Friends.
As far as movies go: Just watch every Ghibli title in their release order. Start with Nausicaä, which is pre-Ghibli but still the spiritual first entry in the set.
If someone has never really seen any anime before, I think Mushishi is a good one to recommend to people. It doesn’t contain any of the less-palatable anime tropes, can be enjoyed by any age group, and is just overall really chill and interesting. It’s also episodic, so if they watch 2 or 3 episodes and decide it’s not for them, they still get a full story without missing out on anything.
The anime spectrum is so vast that the safest bet is recommending a Miyazaki film like Spirited Away or Ponyo. Then, just when they’re hooked, you hit ‘em with Grave of the Fireflies.
Can’t not list Fullmetal Alchemist: Brotherhood
For a gaming anime, either Shangri-La Frontier or Log Horizon
For romance, either HoriMiya or The Angel Nextdoor Spoils me Rotten
For god-tier binge watchers that are okay waiting for a long term payoff of storytelling: One Piece.
I hate to be that guy but calling One Piece god tier story telling is insane
Can’t agree on Angel next door. It’s basically an incel fantasy???