A critical issue.

I'm not an anime expert by any means, but I can name a few works that I like.

For me:
All of Miyazaki. Especially "Castle in the Sky" and "The Wind Rises." The first one is great because of its atmosphere, and the second one is very realistic and historical, with cool references and a touching story (although that's always the case). Oh, and... well, basically all of Miyazaki, just all of it. The most "out there" ones are probably "Spirited Away" and "My Neighbor Totoro." All of them are "out there" in a good way, of course. There's also the series "Future Boy Conan," which I recently talked about.
"The Journey of Kino" – I already praised it. I'll praise it again.
"Grave of the Fireflies." A very sad film about World War II and Japan.
"Wolf's Rain" – I watched it a long, long time ago, and I liked it back then. But I wouldn't recommend it with complete confidence now, because even then there were complaints (mainly about the setting). Maybe if I watched it now, I would like it less.
"Shaman King." Don't watch the anime, just watch the intro instead. Well, actually, you can probably watch the beginning... I don't know how many episodes there are. Because it really goes downhill in the middle, and in the beginning, it's just okay.
"Little Witch Academia." Well, it's very cute and pink... I don't think you, Nebo, would like that level of cuteness. Or maybe you would? But I liked it, anyway. It's not the best, but there were definitely some cool moments.
"My Hero Academia." A successful superhero setting, and it also pays a lot of attention to the psychology of the characters, which is currently very enjoyable. I'm finishing the second season (or rather, I'm waiting for it to finish).
"Pingouin à la Plage." Okay, okay, I'm just kidding, I'm getting carried away.
"Sword Art Online." I just remembered another one. I liked the first arc (half of the first season). But after that, my reader, you'd better not watch it. I really don't recommend it. Seriously, I warned you.

Not anime, but similar in style.

"Tails of a Fox." I haven't seen the whole thing, probably the last 2/3. It's a Korean thing, and I liked it.
"Wakfu" (especially the first season). Oh, this is just a trend of the last few days; originally, Locken got everyone hooked. It's French, which is good... The French are good at making movies, and this is no exception. Humor, spectacle, dynamics... And another plus is that the characters speak that magical language.
"Dofus, Book 1: Julie." In the same series as "Wakfu."