Films I have to agree and say that the person should go with something from Miyazaki. I watched my first Miyazaki film as a kid, so i'd say you don't even need to necessarily tailor the recommendation by the person's age. Princess Mononoke is my personal favorite film by him and easily one of my favorite films of all time, which I watch multiple times a year, but the person could just as easily go with My Neighbor Totoro or Howl's Moving Castle. The selection really is just that amazing. As you get older more things will stick out to you and you'll probably learn more about Japanese culture in general, especially if you're interested in anime, but that just makes the experience better.
If I were to step out from that specific catalogue i'd also suggest The Girl Who Leapt Through Time. Good blend of fantasy and romance, which takes the idea of short range time travel and doesn't use it on some universal scale. Great concept and also a film I rewatch on a regular basis.
Series are a lot harder, because less of them are universal to me and I think that's really something you have to go for. Usually when someone asks me for a recommendation I begin by asking what their favorite genre is, because for some people I would suggest a Gundam series, for others I might suggest Samurai X, and another person might get History's Mightiest Disciple. I think Attack on Titan is a solid suggestion that a lot of people would go for and let me also throw Cowboy Bebop into the ring. I think Fullmetal Alchemist Brotherhood could work as well. Longer than Bebop and really requires you to actually pay attention to the plot, since everything connects, but it really will prepare you for the vast world of anime you're about to get involved in. Great animation and music, combined with an interesting storyline and powers/abilities that are well used.
Honestly, if I knew for a fact the person liked Mecha then Gurren Lagann would be it for something that you can really blow through quickly.
", but these joints that people claim leave them in shambles have almost never broke me down.
