Most anime comes from a known studio as a spinoff of a popular manga. Other works come directly from creative groups, such as Gainax. Utena doesn't fall into either of these categories.
Be-Papas (ビーパパス) was assembled by Kunihiko Ikuhara in 1996, specifically for the creation of Utena. Though it dabbled in other projects afer (see Miscellaneous Stuff), its primary purpose was met with the creation of the television series and its spinoff projects, such as the movie and game.
The story, as best it's known, is that Ikuhara recruited Enokido and Hasegawa after successfully working with them in the past on Sailor Moon, to work on a new project that would capitalize on Sailor Moon's success and allow Ikuhara more creative freedom. As a fan of Saito's work, he recruited her as well, though they had never worked together. Kaneko was brought on for episode direction and storyboards, and Oguro of Studio You became responsible for production and marketing. J.A. Seazer was Ikuhara's prize recruit, perhaps; a musical theater writer and stage director that had held Ikuhara's interest for over 20 years before working with him on the Utena project.
Of course, it's hard to say exactly who is counted among the members of Be-Papas. The bulk of the creative effort seems to have been Ikuhara, Saito, Enokido, and Hasegawa, who were the ones primarily responsible for the development of the concept. I list here everyone mentioned at one point or another as a member, though. Note that the credit lists are incomplete, and are primarily to illustrate other projects they've worked together on.
Enokido was responsible for the series composition and the scripts for episodes 1-5, 7, 9, 13-15, 22-23, 25-26, 30, 33-34, and 37-39. He also wrote the original screenplay for the movie.
A few other anime credits:
FLCL (OAV): Script and Novelization
Gunbuster 2 (OAV): Screenplay (eps 1-6)
(The) Melody of Oblivion (TV) : Series Composition, Script ((1-26))
Neon Genesis Evangelion (TV): Script (eps 2, 7-8, 11)
Nodame Cantabile: Paris (TV): Series Composition, Script
Ouran High School Host Club (TV): Series Composition
RahXephon: Pluralitas Concentio (movie): Screenplay
Sailor Moon S (TV): Script (9 episodes)
Sailor Moon SuperS (TV): Series Composition, Script
Sailor Moon SuperS Movie: Black Dream Hole : Screenplay
Star Driver Kagayaki no Takuto (TV) : Series Composition, Script (eps 1-25)
As you can see, Enokido has been associated with several Gainax projects, and also worked on Sailor Moon; the latter is probably how he met Ikuhara, though his work on Evangelion can't have hurt his cause, since Ikuhara is a friend of the director. Many of Enokido's projects have turned out to be popular for their twisting of a theme or a genre, and where he appears in interviews, he reveals himself to be the likely source of some of the humored cynicism in the series. Fun fact: Enokido and Ikuhara went to the same high school, in the same year.
Hasegawa was resposible for character design, in conjunction with Chiho Saito, as well as art direction. The unusual style of the character animation, both in the series and movie, would appear to be his contribution. Officially, he's credited with: character design, animation director (ep 1), and key animation (OP, ED2) for the series, and storyboard (part D), character design, art director, and chief animator for the movie.
A few other anime credits:
Azumanga Daioh (TV): Key Animation (ED)
Di Gi Charat - A Trip to the Planet (movie): Key Animation
Digimon Adventure: Bokura no War Game (movie): Key Animation
Dragon Ball Z Movie 6: Return of Cooler: Key Animation
Dragon Ball Z Movie 7: Super Android 13: Key Animation
(The) Girl Who Leapt Through Time (movie): Key Animation
Grappler Baki (OAV): Key Animation
Ikki Tousen (TV): Character Design
Leave it to Kero! Theatrical Version (movie): Key Animation
Living for the Day After Tomorrow (TV): Chief Animation Director, Animation Director (ep 12)
(The) Melody of Oblivion (TV): Character Design, Animation Director (ep 24), Key Animation (ep 24)
Neon Genesis Evangelion (TV): Animation Director (eps 5-9) (eps 9, 16), Animation (OP), Key Animation (6 episodes)
Neon Genesis Evangelion: The End of Evangelion (movie): Key Animation Supervisor, Original Picture (ep 26)
Okusama wa Maho Shojo (TV): Character Design, Animation Director (ep 1)
Otome Yōkai Zakuro (TV): Character Design, Animation Director (OP; ep 1)
Sailor Moon R Movie: Promise of the Rose: Key Animation
Sailor Moon S (TV): Animation Director (3 episodes)
Sailor Moon S Movie: Hearts in Ice: Animation Director
Sailor Moon SuperS (TV): Animation Director
Sorcerer Hunters (TV): Key Animation (OP)
Winter Garden (special): Character Design
Zero no Tsukaima: Futatsuki no Kishi (TV): Animation Director (ep 6), Key Animation (eps 1, 12)
Some of these may look familiar! Hasegawa and Enokido have worked together a few times, and both, again, on Sailor Moon and then later on Evangelion. The anime industry is quite incestuous. Apart from joining Ikuhara and Enokido in their lechery during interviews, Hasegawa is apparently a huge sake fan.
Birthplace: Kanagawa, Japan
Blood Type: Type A
Ikuhara is officially credited as the series and movie director, and is responsible for the original concept of the movie. He also dabbled in storyboards in the movie and for episode 1. He is an uncredited vocal on some of the duel choruses, and also supervised the dramatization of the story for the musicals. He is the voice of the art teacher in the movie.
A few other anime credits:
Akuma-kun (TV): Assistant Director (6 episodes)
Gunbuster 2 (OAV): Storyboard (ep 2)
Kingyo Chuuihou! (TV): Episode Director
Magical Taruruuto-kun (movie): Assistant Director
Maple Town Stories (TV): Assistant Director (6 episodes)
New Maple Town Stories (TV): Assistant Director (6 episodes)
Nodame Cantabile (TV): Storyboard (OP), Episode Director (OP)
Sailor Moon (TV): Episode Director (8 episodes)
Sailor Moon R (TV): Series Director (eps 14-43), Storyboard (4 episodes), Episode Director (eps 51, 60-61), Art Director (ep 68)
Sailor Moon R Movie: Promise of the Rose: Director
Sailor Moon S (TV): Series Director, Storyboard (4 episodes), Episode Director (4 episodes)
Sailor Moon SuperS (TV): Director, Episode Director (5 episodes)
Soul Eater (TV): Storyboard (ep 29)
Sweet Blue Flowers (TV): Storyboard (OP)
Ikuhara is more or less the face of Utena's creative team, garnering the majority of the interview time. He has toured anime convention circuits extensively, often with Chiho Saito, and so is well known to the American fanbase. As what, it's hard to say; he's an eccentric figure, known for terrifying cosplay, evasion of questions, and no small amount of lechery about lesbianism, even while swearing it's not really there. He is responsible for the recruiting of J.A. Seazer for the duel choruses. And he is, like all decent human beings, a cat person. He went to high school with Enokido, in the same year. Ikuniweb is his website.
Oguro is credited for 'planning', which could mean a million things. Judging from his staff credits, and his being the connection between Be-Papas and Studio You, an advertising company, he was likely in charge of production and marketing, but with his history of also dabbling in writing, he may also contributed to the brainstorming.
A few other anime credits:
Doki Doki School Hours (TV): Marketing Cooperation
Gekiganger 3 (OAV): Script, Story
Goku Sayonara Zetsubō Sensei (OAV): Series Composition
Hanamaru Kindergarten (TV): Series Composition, Script (eps 1-6, 8-12)
Kemonozume (TV): Literature, Planning Assistant
Zoku Sayonara Zetsubō Sensei (TV): Series Composition
As planning and production, Oguro's primary task appears to have been making Utena happen, and getting the rest of the creative team's idea approved and pulled together. According to the recent Nozomi release of the first season of Utena, he was the editor for the Japanese laserdisc release of the series, which included extensive artwork and liner notes. He does have a twitter account: animesama.
Birthplace: Kodaira, Tokyo
Blood Type: Type B
Saito wrote the manga for Utena, which was released alongside the show as a seperate imagining of the story. The character designs for the show and manga were collaborations of sorts between her and Hasegawa, with her drawing concept designs that Hasegawa later adapted. The manga appears to have been done the same way, with Saito's manga incorporating the same themes as the movie, but approached from her own style.
A few other manga credits:
Anastasia Club (manga): Story & Art
Aru Hi, Knigh ni Attanara (manga): Story & Art
Basilisk no Musume (manga): Story & Art
Bronze no Tenshi (manga): Story & Art
First Girl (manga): Story & Art
Gin no Ookami (manga): Story & Art
Honoka ni Purple (manga): Story & Art
Kakan no Madonna (manga): Story & Art
Kanon (manga by Chiho Saito): Story & Art
Koi Monogatari (manga): Story & Art
Lady Masquerade (manga): Story & Art
Magnolia Waltz (manga): Story & Art
Senichiya no Kagi (manga): Story & Art
Tenshi no Bishou, Akuma no Namida (manga): Story & Art
Tenshi no Tattoo (manga): Story & Art
Waltz wa Shiroi Dress de (manga): Story & Art
(The) World Exists for Me (manga): Art
Saito is often interviewed alongside Ikuhara, and in these interviews frequently jokes that the stranger things in the series were not her idea. Nevertheless she's an obvious contributor, with the European aesthetic and penchant for Indian characters seeming to come from her.
A biographical piece written by Claire Samuels for The Black Rose Blooms, one of the Central Park Media DVD releases, summarizes:
Real Name: Terahara Taka'aki (寺原 孝明)