If I don't have the category you want beta'd on my list, just send me a message. Chances are, I'll beta your story anyway, if you really want me to. I'm more likely to say yes if it's a one-shot.
Things not on my list that I am mostly familiar with:
Supernatural (up to season 5)
Teen Wolf (up to season 3)
Marvel movies (and if you've got a Darcy Lewis fic- Give. It. To. Me.)
I like to make sure that things flow smoothly- ie. no constant periods. This might cause some minor re-arranging of a sentence, but nothing that will impact the story. I also catch double words, the differences between the "theirs" "yours" and the "toos" as well as attempting to fix/point out sentences that don't make sense due to awkward phrasing or inappropriate word choice.
I can offer critiques too, but it's something you have to ask for. I word most of my critiques like this: "this paragraph would have a much higher impact if you re-arranged the sentences into something like this." Or, "your plot is amazing so far, it just seems like the characters are able to get everything done so fast. Maybe instead of having them jump from action to action without really explaining things, you go into a bit more detail here."
I always bold all sentence structure changes I make, and place them within parenthesis so that you can see what you've written, and how I'm suggesting you change it up. Everything I put is always 100% a suggestion, and in no way is something I feel you have to do. Also, I will not get upset if you use my suggested sentences verbatim in your fic, so long as you give credit to me as your beta reader (you do not have to give credit for the specific sentences, just a mention that I am beta reading).
I have also had many people concerned with fic theft, and I understand this fear. I want you to feel comfortable sharing your story with me, and am willing to work with you on any safety measures you feel are appropriate.