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 am also a huge sentimental marshmallow and enjoy getting weepy about feelings.
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.
For more reference on my preferences, I mostly hang out on Tumblr these days, where I mostly reblog pretty things and occasionally ramble.
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.
Mysterious Mr. Quin - Agatha Christie - Mr. Harley Quin, Mr. Satterthwaite
There's not really a delicate way to say I SHIP IT I SHIP IT A WHOLE LOT THEY SHOULD KISS. Well, there's probably a more delicate way than that, but, anyway.
I'd love casefic after the fashion of the book, and/or an exploration of the book's mythology, or for a change a story that show's Mr. Quin's perspective on Mr. Satterthwaite.
I find this book absolutely fascinating. I love the way Christie takes a Harlequin motif and runs with it in what very much looks like an actual-avatar-of-death direction, avatars of death getting involved with humans being one of my bulletproof narrative kinks. I like the sort of understated but growingly undeniable aura of the supernatural that stretches through the stories. My favorite one, I think, is "The Man from the Sea." I generally like the quieter, smaller mysteries, that are less about murder and more about just people. (Though, like anyone, I like a good murder.)
And all of that is potentially irrelevant because I also just absolutely adore Mr. Satterthwaite. Being, as I mentioned, a complete marshmallow, I find him deeply relatable. I love that he's both an excellent detective and kind of dithery and gossipy, that he's old-fashioned and Victorian but not so much that it prevents him evaluating contemporary art on its own merits, and I'm a great fan of the way he is sort of a less ruthless detective than, say, Poirot or Miss Marple, but just as ready to get things done.
Speaking of other Christie detectives, I wouldn't mind basically any crossover, aside from Poirot, since that's been done, but perhaps Miss Marple, or Tommy and Tuppence, or Superintendent Battle. (I've read basically every Christie novel there is...)
The Lost Conspiracy - Frances Hardinge - Hathin
I just love Hathin so much it hurts, and I would love to read any post-canon fic about her growing up and coming further into her own. For example topics, her involvement in rebuilding, her evolving relationship with Arilou, her coming to terms with her own celebrity status, even her leading a right proper revolution against the Port Suddenwind government.
I don't even know what else there is to add. I love everything about this novel: the worldbuilding, the use of language, all the diverse characters, and above all Hathin herself. I would read anything about her.
Tricksters - Tamora Pierce - Alianne Cooper, Kyprioth
I love these books mainly for the politics and for Aly's trickiness. I'm really into her scheming ways and the how she can be so much darker than the other Tortall heroines, and I love the way her relationship with Kyprioth both brings that out and sometimes makes her push against it when he crosses her idea of boundaries. I'd love any story exploring their relationship, perhaps with Aly getting wise to one of Kyprioth's schemes she hasn't been made privy to and either interfering or helping, or Kyprioth coming around to meddle in Isles politics some more.
And, yeah, I do ship it, but if you don't or can't find a way to make it work in your story, that is totally fine. I just sort of have a thing about humans in messy relationships with more-than-human entities, it's a bit of a running theme.
Some of my favorite other characters in this series are Dove, Winna, Taybur, and Dove. (Seriously, if you get stuck on this prompt and want to write about Dove as Queen, I would not be the slightest bit put out.) I do have a slight problem in that I don't care for Nawat or Aly/Nawat, so if you could keep him to the background as much as possible, that would be lovely.
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.