I am so happy you've chosen to write for one of these dear fandoms of my heart, and I hope you'll enjoy writing it, as I'll no doubt enjoy reading it.
I love banter, and plotty fics, and broadening and exploring canon worlds, and fabulous female characters, and atmospheric prose, and exploration of relationships, and keeping to the spirit of the canon while going beyond it. I have a particular fondness for things that play around with language or make up tricky legal details for fictional worlds, but obviously if those aren't things you feel comfortable writing, I will be just as happy. I do enjoy just about everything, barring a few caveats. To wit: I don't particularly like explicit sex or violence, angstfests, or tacked on childhood trauma. And my one and only throw-the-book-at-the-wall-in-fury plot element is magical memory loss, especially as an end point. I'm otherwise rarely picky about content, except where it's wholly inconsistent with the original work.
Basically, do what feels right, ignore whatever parts of this letter aren't working for you, and have a lot of fun!
And now on to specifics.
Robots - Isaac Asimov - Susan Calvin, Stephen Byerley
Dr. Susan Calvin is my favorite character of all the Asimov universes, and that is no small distinction. I love the way she pretty much made up her own dream job and is so consistently amazing at it, and how she takes no bullshit. I will love any story you choose to tell me about Susan being her brilliant, caustic self, be it adventures in malfunctioning robots, in US Robots upper management personality clashes, or in robot-related political maneuverings and pitfalls.
I'd love it if Stephen Byerley were involved, particularly if it were set during his term as mayor -- because robot mayor of New York is an irresistible delight, and "Evidence" is my favorite I, Robot story, if any of them are. I love the snide political remarks in the narration. Not to mention being totally fascinated by the application of real-world circumstances, especially law, to a science fiction setting ("Bicentennial Man" is another Asimov work that really strikes a chord with me), except of course it isn't, really, in I, Robot, at this point it's near-contemporary New York, which is a little circumstance that amuses me, given the distance between the projection and the reality.
I also love the relationship we see between Susan and Stephen in "Evitable Conflict." If you can find a way to make romance between them work, I would be enthralled, but obviously that's not in any way necessary. Just give me some nice Asimovian hijinks. And if you get very stuck, I would never say no to The Adventures of Stephen Byerley, Robot DA.
Kings - Rose Benjamin, William Cross
I really just want some good old messed up sibling-fic. I'm entertained by William's absolute loathsomeness and the way he be so petty while being ruthless, and I love Rose's take-charge, doing-this-for-your-own-good style of family management and her sense of performance, and the way she's prepared to step in and rule when Silas can't. Basically I guess if you were going to focus more on one of them, I'd prefer it to be Rose.
Of all the family dynamics we see on the show, Rose and William get relatively little focus, and I'm very interested in seeing how their relationship plays out, especially when they're younger. Did they get along as children and young adults, or were they at odds? Were their interests more aligned before they both had children, and other conflicting loyalties? How exactly did the negotiations surrounding Rose's marriage to Silas work? Was Rose involved in operating CrossGen before she was queen? If you wanted to take this to the incest place, I would be okay with that, but, obviously, don't if you aren't comfortable with it.
My absolute favorite thing about this show is the stylized, mythical dialogue it falls into for many of its central scenes. The epic, biblical proportions of the story, the use of signs and portents, all are really appealing to me against the backdrop of a modern setting. I'd really enjoy if the story explored in part the recent history Gilboa, the wars and the building of Shiloh and so on, and the way the world works in general.
Mysterious Mr. Quin - Agatha Christie - Mr. Harley Quin, Mr. Satterthwaite
I'm fascinated by this collection, representing as it does Agatha Christie's dabbling in magical realism. The juxtaposition of small family dramas wit the looming presence of death is one of the things I like most about her work in general, but actually getting a physical manifestation of Death involved -- and that's how I read Mr. Quin, ultimately -- is taking it a step further, and incredibly compelling to me, because "personification of Death gets attached to mortal" is my favorite plot. So there is that aspect of it that I really love, but on the other hand, I did pick the book up in the first place, all unsuspecting, because I'd really enjoyed Mr. Satterthwaite in Three Act Tragedy, and I absolutely loved hanging out with him in his natural setting, that is, the small-scale, intimate, gossipy drama. I love the way he's simultaneously a perfect society insider and a perpetual outsider as regards life itself, and I enjoy the literary and artistic references that litter his conversation, and his patronage of the arts that despite his deep Victorianism allows him to evaluate modern works on their own merits. Ultimately what I love is the tension between, on the one hand, the limited scope of the stories, represented by Mr. Satterthwaite, who is very much a person, with his history and his foibles, and on the other hand their broader significance and the influence of the supernatural, as represented by Mr. Quin, who is in many ways a plot device much more than a character.
Oh, so, what I actually want, is just more story, that explores the themes outlined above. Anything that follows the basic tone of the book, though I would love to see a more in depth look at the supernatural elements. Obviously you have free rein to make up a bunch of original characters and tell me some fascinating story about them for Mr. Satterthwaite and Mr. Quin to become involved in.
Having written that whole digressive essay, I now realize I neglected to mention that I ship it like burning. Which, now that I've mentioned it, you're free to ignore, but, y'know, useful information.