hi anon!

These write-ups take a while, so thank you for your patience! I always want to make sure I’m really thorough with them. I hope it's alright that most of my answers are going to be !-era: they're easier to access, and easier to list! The summaries will be vague so as to pique curiosity but not spoil too much.

Reading order really just depends on how you like being introduced to groups:

a) If you want to start with lore-heavy stories to see Akatsuki’s formation and development, I suggest working from fundamental readings downwards to the group stories.
b) If you prefer lighter, fun stories, then I suggest starting with the group stories, and working your way backwards to the fundamentals.

As little extras, I’ve also included recommendations for each member, and stories that involve other units. I'll structure these topics like a choose-your-own-adventure, just to mix things up!

(Big disclaimer before we start– This list is not every story out there. I’m a Keito-P with a Ryuseitai bias, so I’m most familiar with their stories. Additionally, my biggest blindspots are AKATSUKI (Kuro) and Valkyrie and AKATSUKI and UNDEAD, so while they have good stories out there, I either haven’t read them or aren’t as familiar with them as I’d like to be.)

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Fundamental AKATSUKI reading
These are absolutely key to understanding AKATSUKI’s formation, development and current state. Be mindful of content warnings: these stories can get heavy.

Chronologically, this is their order (though Meteor Impact takes place over three years):

Crossroad (War-Era)
(UNDEAD + AKATSUKI)
Crossroad is the origin story of UNDEAD and AKATSUKI. It primarily covers the degradation of one relationship (Rei and Keito) and the construction of another (Keito and Kuro), as Keito tries to kick off his and Eichi's War.

Crossroad is getting an anime adaptation in November!

Meteor Impact (War-Era)
(RYUSEITAI + AKATSUKI)
Among many other things, Meteor Impact is the origin story for the creation of the student council (Keito and Chiaki), Akatsuki’s role in the war (Keito, Kuro, Souma), and the reason for Kanata’s entire subjugation + Battle of the Sea God (Akatsuki v. Kanata).

Shinsengumi
(MaM + AKATSUKI + Subaru, Hokuto, Eichi, Tsumugi)
AKATSUKI and MaM hold a joint live concert, with extras involved. This story is Kuro and Madara-heavy, and covers the fallout after the War, where Kuro considers AKATSUKI currently stands, and Madara’s schemes in present-day.

Quarrel Festival
(fine + AKATSUKI)
Eichi provokes Keito into facing off against fine: the penalty for loss– AKATSUKI’s disbandment. This is a critical story where AKATSUKI recontextualizes their role from a war-era artifact to a group that actively wants to pursue their dreams together.

Group Stories
These are more of your “feel-good”, slice-of-life stories. They contain lore, but they’re short, fun and easier to read.

The Spectacular Cinderella Show
(Wataru, Tomoya, Hokuto + AKATSUKI)
The Drama Club is putting on a show for the school festival, and AKATSUKI tag along as actors in their rendition of Cinderella: Kuro as the prince, and Souma and Keito as the evil stepsisters. Absolutely hilarious story.

Kabukimono
(Kanata + AKATSUKI)
Keito and Kuro are overworking themselves. With the help of Kanata, Souma tries to find a way to ease them of their burdens. Very sweet.

Hanafuda
(Shinobu + AKATSUKI)
When Shinobu and Souma discover a missing playing card in their Hanafuda set, Keito reveals a dark secret: the consequences of AKATSUKI’s prominence in the wartime-era. It’s an interesting story, and one of many where Keito reflects on the extent of their actions.

Cats and the Camelia Train
(Leo, Arashi, Nazuna + AKATSUKI)
Souma finds a stray cat and hides it. When Souma finds out it belongs to a local cat cafe, he takes initiative on hosting a live performance there. Super cute, and it has some interesting character interactions for AKATSUKI.

Underdoctor
Keito needs to fill out an interview about his free time, and realizes… he’s a boring person. Kuro and Souma run into him in the shopping district, and they spend the rest of the day together. Precious, and they all drink boba.

Hopefully that answers your initial question! Below are supplementary stories, in case any AKATSUKI member in particular catches your attention.

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If your favorite is Keito…

… And you want to see him acting as student council vice-president:
Flower Festival
(fine + AKATSUKI + Valkyrie)
The first time the new members of fine meet each other at the beginning of !-era! Keito is actually the one to facilitate their introduction and training, since Eichi is out of commission.

Daikagura
(Trickstar + AKATSUKI)
AKATSUKI and Trickstar hold a New Year’s Live together. It’s heavy on Keito’s role as vice president within the school, and what responsibilities he tends to have. Also very Keito/Mao heavy, as he rears him into the student council president role.

… And you want to know more about his relationship with Leo and Madara:
Concerto
(Eichi, Keito, Madara, Leo)
Leo returns from abroad, and Madara is in town to support him. Keito and Eichi run reminiscence and end up talking with both.

Robin Hood
(Leo, Tsukasa)
Leo tells the story of how Keito was not-so-by the rules when dealing with delinquents who set up camp in the archery hall.

… And you want to see him with kouhai:
Fresh Green Martial Artist
(Souma, Keito, Kuro, Tetora)
A good look at the extent Souma harasses Keito. Absolutely hilarious, had me on the floor the whole time. If you want to see Souma’s absolutely unbridled obnoxiousness, this is… so good.

Biblio
(Midori, Hajime, Keito and Tsumugi )
Keito and the others wait out a rainstorm in the library. This is a story made to soften up Keito’s impression to both Ra*bits and Ryuseitai juniors, as well as establish his relationship with Tsumugi.

Zodiac
(Midori, Keito, Subaru)
Midori finds a dog and… well… mistakes it for Chiaki. Keito makes a brief appearance.

Chinatown
(Sora, Keito, Tsumugi, Makoto)
Under the impression that he’s upset Sora, Keito gets to work in the kitchen to make his favorite dish: hot steamed buns. A personal favorite of mine.

… And you want to see him wet and shirtless:
Comic World
(Keito, Kanata, Kuro, Ritsu)
Kanata enlists Kuro to help him tie up Kaoru’s surfboards during a typhoon, and Keito comes along. At the same time, Keito is trying to pin down who is releasing manga based on him, Kanata and the war. It’s short, but gives good insight on post-war sentiments between Keito and Kanata. And I stress again… wet, shirtless Keito.

If your favorite is Kuro…

… And you want to see him with classmates:
The Wolf and Red Riding Hood
(Nazuna, Kuro, Shinobu, Souma)
Kuro helps Nazuna and the Broadcasting Committee prepare a play for preschoolers. He doesn’t anticipate getting roped into acting himself. Bonus points for Shinobu and Souma.

Opera
(AKATSUKI + Eichi, Wataru + Chiaki, Tetora + Leo)
Akatsuki puts on an opera, and others aim to be a part of it.

Gang
(Yuzuru, Ibara, Mika, Kuro, Chiaki)
When news of a terrorist goes around the school, Kuro gets tense. Great story for Chiaki and Kuro if you’re looking for a post-Meteor Impact read.

… And you want to see him with kouhai:
Tough Guy
Kuro needs help practicing for the filming of a school drama, and Chiaki takes the initiative to go and help alongside Midori and Tetora. They practice lines for a script… and flop terribly. It’s amazing, this story is hilarious.

Four Beasts of Fist Fighting
(Tetora, Kuro, Koga, Keito)
The thesis of this story: “everyone loves Kuro”. This story goes into how Tetora found RST post-Akatsuki rejection, the Dragon King Competition, and why the Student Council broke it up during the Main Story.

If your favorite is Souma…

… And you like Marine Bio Club:
Palace of the Ocean
(Souma, Adonis, Kanata, Kaoru)
Souma becomes enamored with a turtle he names Kamegorou, and spends the story taking good care of it.

Aquarium
(Kanata, Kaoru, Souma, Rei, Wataru, Madara)
When Kanata goes missing, his friends scramble to find him, including Souma.

… And you want to see him with kouhai:
Scroll of the Elements
(RYUSEITAI + AKATSUKI)
Souma takes initiative to help Shinobu execute his proposal for a joint live show as ninja and samurai. It’s a great story to see them in action together: they’re very close.

Summer Night Festival
(Ra*bits + AKATSUKI)
AKATSUKI and Ra*bits prepare for a joint live together. While Keito and Nazuna take one direction on their show, Hajime wants another. This one is Hajime and Souma-centric, and there’s good Nazuna/Keito content too.

Colorful Autumn
(Midori, Tetora, Kanata, Souma)
Tetora, Souma and Kanata help Midori paint signboards for his family’s grocer. There’s a lot of cute direct interactions with them here.

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Stories with other Units

UNDEAD
Decorate
AKATSUKI needs help learning how to be charming for their Chocolate Festival. UNDEAD steps in as their coaches. Bonus points for the return of Keito’s ‘bakyu~un’.

Athletics
UNDEAD and AKATSUKI participate in an athletic training variety show together. Great for Adonis/Souma, while Koga/Keito strike up a rivalry in the background.

Rabbits
Tanabata Festival
If you’ve seen the anime, this is the story it adapts. The best part is that AKATSUKI is way softer in the original version: The Rabbits juniors are astonished that Nazuna is so well-regarded, and AKATSUKI makes up for their actions in the main story.

Summer Night Festival

RYUSEITAI
Scroll of the Elements
Souma and Shinobu take the lead planning a joint live together, and RYUSEITAI and AKATSUKI follow suit. It’s a good foundation for where the two units stand with each other after the events of Meteor Impact.

Submarine
This is the only !!-era recommendation on this list, just because it came out recently. If Meteor Impact is pt.1, and Scroll of the Elements is pt. 2, this is pt. 3. Highly recommend, especially because of Souma’s war tactics in Okinawa.

Trickstar
Daikagura

Miscellaneous
These are so good, I can’t not include them.

Crash Course
(Shinobu, Yuta, Hajime, Tori, Keito, Wataru, Souma, Kanata)
Idols from different units pair up together to learn from each other. Souma and Kanata pair together… and Wataru and Keito pair up together. Absolutely delightful.

Diner Live
(Leo, Eichi, Kuro, Nazuna + Wataru, Izumi, Keito, Madara)
An even funnier read if you like Wataru/Keito and !-era shuffle units. In response to Knights Killers’ formation, Wataru conducts a shuffle unit of his own: Traumerei. Bonus points for Kuro acting like a kicked dog at the prospect of fighting against Keito.

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I hope this helps! They’re very simple descriptions compared to my RST + AKTK write-up, but this is more of a standard recommendation as opposed to dynamics needing explanation. Thank you for asking, anon!

(I should really make a large graphic about all the intersections AKATSUKI has, so a project for another day!)