FMA, both versions, have an interesting premise with interesting characters as the manga expands on the female characters more than the 2003 version. Both tackle the same themes but 2003 deconstructed and more cynical. For the love of Godoka, just read the manga and save the trouble of watching the first episode. FMA is my favorite but I’ll not take the first episode of FMAB or anything that seriously didn’t begin how the manga actually started and introduced the world as it is. This is why I’d rather have the manga over the physical DVDs of FMAB.
Anyway, there is still so much weirdness to get through no matter how constructed and natural they are.
Would a good story make them take the weirdness? What is a good anime that provides those in doses?
There are flow charts out there.
However, these flow charts still don’t allow an easy grounding of what an animanga can have at its best. We have to respond with as little fanservice as possible.
While it is nice to introduce all the gems and underrated gems, it’s best to start off with what kind of anime they would like, judging by their preference. It’s great to expand their horizons but best to do it slowly.
People in the West might prefer to see an anime based on the West like any particular century. Even something familiar with superheroes or anything resembling Western culture in the zeitgeist.
Violet Evergarden and Attack on Titan are good Western-based entries.
Because for better or worse we’re introducing them to the better ones, they likely see and want the best. That is if they understand
Jujutsu Kaisen is a good beginner anime as I list that requirement. Honestly, skip that since it’s better to watch the predecessors to understand the genre conventions JJK is subverting and deconstructing.
If you can stand fanservice, particularly for the minors on the heroes' side, then MHA is also a good choice erring from Bakugou's S6 beginning moments and cuts to the MVA arc.
Perhaps Hunter x Hunter and YuYu Hakusho are good ones. Watch this then watch JJK.
I do not like the author now but look at Rurouni Kenshin.
As much as it pains me, SAO is a good choice. I'd prefer they go see the Progressive films than the original series but Godoka, it's such a beginner anime.
As basic choices as they are great, Cowboy Bebop and Trigun are excellent choices. These are notably Western based so it’s a plus there.
What about Psycho-Pass? I know the police is a hot-button but this is a good show.
If people like or are willing to take a chance with different art styles, One Punch Man and Mob Psycho 100 are definitely good choices.
Hmm, Persona 4 the Animation and Persona 3 movies will at least be decent introductions too. Notice I did not say P5 the Animation, just watch Proof of Justice and The Day Breakers OVA, the only P5 the Animation things I will recommend.
While it does little fanservice with Thorn Princess Yor, Spy X Family is also a great beginner anime. In addition, it's a great adaptation of the manga on top of it too.
For an underrated series, Katekyo Hitman Reborn is a good one. It started as a gag manga but into shounen territory once hit the Varia arc. There’s little fanservice there albeit women on the sidelines though there are some women on the battlefield.
What about Shoujo, aiming toward the Kdrama crowd? Fruits Basket is a great choice. Ouran High School Host Club is also a good one even if it's not that faithful. However, these choices just aren’t quite there even if they are good. Classic shoujou is better to understand the new entries so Inuyasha is a better choice.
Magical girls are somewhat easier as Puella Magi Magica Madoka is renowned. However, CCS is a good choice for good old-fashioned magical girls. The 90s Sailor Moon is also one if it weren't for the fact it's long and not very faithful to the manga. Crystal is more faithful.
I’m trying to recommend classic magical girls here so you can understand the deconstruction.
I love Kamen Rider Gaim and Fate Zero but those are deconstructions within the series itself.
Sports anime is easier to understand and get across the Japanese culture. Haikyuu is a good choice. Yuri on Ice is also a good one but it does require a bit more how sports anime work.
As for gag, Katekyo Hitman Reborn started out as a gag manga because there was initial controversy about it transitioning into shounen.
If they are willing to suspend their disbelief even further, then SK8 the Infinity (the first skateboarding and not just a scene or a hobby!) and Kuroko no Basuke (if you are willing to see superpowers and rule-bending). If you really want superpowers in your sports and defy gravity for the most part, this is the way to go I suppose.
Harems get a bad rep even outside. My Next Life as a Villainess is a good one. Re:Zero is also a good one but it’s a deconstruction. Konosuba is also a good one but it’s a parody. I really should recommend classics so you can work your way up to the newer entries so
Let’s see about LGBT and BL. Notice I am trying to differentiate so that people know what to look for. Yuri on Ice is LGBT and best recommended. Sasaki and Miyano is the BL choice. If you want one of the better written of the entire BL, go for No. 6. I still have a fondness for the show as it and Tokyo Babylon introduced me to BL. Seriously when I was a kid, I wasn’t shipping guys together until I was starting to question myself. I was too busy with heterosexual ships to even consider which is ironic when my first complete manga was Tokyo Babylon. It was part of my CLAMP needs at that time but I know for certain I read all 7 volumes.
Now that I mentioned Re:Zero, isekai are oversaturated but it should still be the best beginner anime.
As for Mecha, I want to make it clear that Mecha has been anti-war expressively from the start. There are lots of politics but the point is anti-war. Yeah, there are child soldiers but Gundam is fully aware. EVA is a deconstruction but focused more on mental health as this is Hideaki Anno's mental health on full display here. The End of Evangelion was written by a person not in a good place at the time. Gundam Iron-Blooded Orphans is a good starting mecha. If fanservice and the development of women are only doable, Code Geass is a good one. This is why VLD was such a bad mecha because it was never mecha in the first place as it was created and written in the USA, the glorification of war and not even thinking of the casualties of war from the other side was never bought into question and the 'war' part was skimmed through that none were able to feel the impact in the final seasons. It’s sci-fi but bad sci-fi. Honestly, why am I mentioning VLD when it’s not even a Mecha series but a sci-fi series that tried to be ATLA but worse because it's a series that don't know the basics of writing?
Anyway, Macross Frontier is also a good choice.
While Mecha can be easily explained when we got Pacific Rim which also understands the point of the mecha in the first place which is anti-war, Moe is harder to explain. Bocchi the Rock is obviously a great choice.
I'm trying not to recommend deconstructions. MDZS is a deconstruction of the xianxia genre so really it isn't a good starter to knowing the genre.
Madoka is a deconstruction just as MHA is a recon-deconstruction old-school callback of both classic shounen and superhero tropes of both the West and Japanese variety (super cops basically as they are always depicted as an auxiliary/paramilitary force in Japanese media. See also Tiger and Bunny and some Super Sentai entries). Death Note is a deconstruction of the Shounen formula. Evangelion is also a deconstruction which makes it ironic because EVA was my introduction to mecha which was crystallized with Code Geass. I watched Gundam and Macross way later.
It's not that you can't enjoy the deconstruction of a genre at first taste. It's a deconstruction of a genre in which these genre conventions are already in place; complaining about not knowing the genre conventions is stupid when it's a deconstruction.
I love Princess Tutu, Revolutionary Girl Utena, and Mawaru Penguindrum but they are staunch examinations. These are arthouse and require lots of brainpower with all the metaphors. PT is still better off though as it used fairytales and ballet. Still, these are deconstructions though Utena is both common anime and fairytale tropes.
In a similar manner, just don't watch Gintama until you see enough of animanga. Gintama parodies a lot.
And those are on series. Movies seemed to be better introductions.
Studio Ghibli is the obvious choice. I really don’t want to recommend The Wind Rises because imperial Japan to Korea is there. I’ll take the 3D film over that even when the 3D film is not that great and lifeless.
Makoto Shinkai and Satoshi Kon are directors I recommend checking out their filmography.
Ghost in the Shell and Akira are great choices to dip toes in tentatively.
Non-canon films from popular franchises are standalone. Maybe knowing the characters is not enough but I could still recommend it if the movie was interesting enough to seek out the franchise.
Baron Omatsuri and Red are definitely good films to look into for One Piece. Red is the closest to canon that you can get.
As for Detective Conan, I would say Phantom of Baker Street, London VR before the actual London arc in canon. I’m hesitant to use the Black Organization/FBI/PSB ones.
Each Lupin film is standalone as Lupin III is a folk character, malleable to an interpretation needed. The Castle of Cagliostro is a good one as it's also Hayao Miyazaki's film too. Lupin III The First is also a good one as well as having CGI that puts Pixar to shame. Seriously, it showed CGI can be used for more cartoon fare that is told in a better story with better purposeful cinematography.