These are fairly short prompts, as they're mostly fairly "anything goes". With the exception of The Musketeers I have a fairly detailed writeup for the fandom in my tags.
Do Not Wants: Rape (most things that fandom likes to dub non-con would fall into that with me), romanticization of jerkish/abusive behavior, including of the "needs the love of a good woman to redeem him" varieties (mostly safe with these fandoms), slut shaming, women fighting over a man, sexual harassment being funny/cute/sexy. I'm also not big on adultery/cheating, though make exceptions for estranged spouses, or people stuck in arranged marriages that make them unhappy. (It would be hard to like almost anything canon in The Musketeers otherwise.)
Fandoms:
AKB0048
This is actually the one I want the most, and also the one with the smallest fandom. However, teenaged girls who run around being joy and spirit to the universe by staging guerrilla concerts, and their microphones turn into lightsabers, which they use while singing. I mean, what's not to love? My favorite characters are Chieri, Kanata, and Yuuko, but I love everyone. If you want want to write something shippy, I like Nagisa/Chieri, Nagisa/Yuuko, Yuuko/Takamina, Takamina/Kanata, and Kanata/Minori the best. I'm fine with most pairings, though would prefer anything with Sonata to be set in the future, given her canon age. Plotwise, anything with the girls working and growing together and dealing with becoming successors and/or graduating would be great.
Gekkan Shoujo Nozaki-kun
THIS SERIES. I love the humor and the meta, and I love Sakura's relationships with pretty much everyone, and how the girls have somehow formed a relatively normal friendship-threesome even though two of them are Totally Out There and the other is permanently hung up on a guy who wouldn't get it if everyone tattooed it across their foreheads. Shipping wise, I'm fine with all 3 girls in any combination with each other, and with their canon love interests. i'd like something with their friendship, either all three or just two of them, particularly if you can find a way to work shoujo meta/commentary into it. (Note: I LOVE shoujo, but also think a lot of it has serious issues, especially some of the most popular series, so no anti-shoujo, please, just in case.) I'm not current with the manga, but will be current with scans by the time stories go live.
The Musketeers
This was NOT a series that I expected to love (I'm not fond of the book, but end up watching most adaptations) but I do. I love Anne and Constance's friendship, and would like something with that, or with one of them having to work with Milady. Shipping-wise, again, fine with the canon love interests, and I also like Constance/Anne. Given the nature of Anne and Constance's respective relationships (non-relationships?) with Milady, I don't really see her with either ,but if you do and want to write it, go for it, i'm not opposed. I admit that, while I like Milady A LOT (and one of the reasons I like the shows is that it considers her POV to be valid and have merit, even when she's at her worst) I don't feel the connection to her that I sometimes do to Anne and Constance.
I will try to remember to come back and edit this once the second series has finished airing.
A Certain Magical Index:
This show (as well as A Certain Scientific Railgun) figuratively ate me alive for a while last year, and I was tearing through fantranslations of the novels when Yen licensed them and baka-tsuki (understandably) took them down, so I actually haven't read past what was covered in the anime. I love all things Misaka (great genetics there) and wish the main 3 (Mikoto, Last Order, Imouto) interacted more. I like Touma and all shipping combinations of Index/Touma/Mikoto, though I'm not big on how all the girls fall for him. I find Kuroko and how she uses her teleportation skills and her devotion to her job very interesting, and I like her friendship with Mikoto, though I really dislike how her crush on Mikoto manifests. I like how Index, despite her hapless appearance, can be almost frighteningly smart and analytical, and I wish her situation regarding her memories and ignorance of the world were treated with more gravity, and less as something to make her seem cute and in need of protection. I wish there was more development of her previous friendships with Stiyl and Kanzaki (especially the latter), or even her just realizing that she used to have important relationships and connections that she can't remember, and wanting to know about them. I find Kanzaki and her nature and how it isolates her at times to be fascinating, and wish there was a lot more of her, or really anything from her POV, as I feel much of her development in the parts of the canon that I've encountered are more from other people's observations of her.
Have fun!