I am a retired, happily married, American male, who has enjoyed reading Harry Potter fan fiction since 2000. During that time I have read some which I am amazed if the writer has passed basic English, and many others in which I am likewise amazed that the writer isn't making a living by selling his/her work. I am not a grammar nor spelling nitpicker, unless it is so bad that it distracts from the story. Like most of us, I have a set of preferences and non-preferences I use when selecting a story or writer to read. Those will be reflected in the list of authors I favor. I know there will be many other excellent writers that I just don't read because they don't happen to write stories with the parameters I like. I have selected a list of authors, as opposed to individual stories, because I have found if an author is good I will enjoy most of his/her work. In addition, I have enjoyed so many great stories on this site that to list them all would be cumbersome. If you agree with most of my preferences then I think you will likewise enjoy these fine writers without having to wade through too many adolescent fantasies where Harry has a 20 girl harem and is endowed with super powers. So, here are my primary preferences:

1. Harry Potter. I like stories in which, at least, one of the main protagonists is Harry. Not that it can't be told from a different POV, or revolve around a different character, but I prefer Harry stories, not James or Harry's daughter Rose. I like my Harry to be male, heterosexual, ages 2 - 20, not pregnant, not endowed with super powers (other than magic, of course), and intelligent enough to make logical decisions which will give him victory over adversity (I'm not so much into pure romance writers).

2. Ships. I have found that most writers write with this criteria fairly consistently. I find I like stories when Harry is shipped with a variety of girls roughly his own age (not opposed to him being with Fleur or Tonks, but Minnie? ACK!) Trying to imagine any older adult as a love interest being de-aged is a thought too far for me. Being with Pansy is also a stretch as she is just too consistently written as an antagonist. What will almost always cause me to skip a story is to see Hermione shipped with Ron. If there was ever an unbelievable pairing, that was it.
3. Time warps/Do overs. Okay, I admit it. I'm a closet do over fan. I especially like Reptilian's challenge where his death angel sends him back for the 7th time with the plea "Do not die early this time!" I smile every time I find one. Perhaps one reason is that he is supposed to not mess up his soul bond with "some Granger girl" this time around, and I really thought that JR missed that ship badly in canon. It amazes me to find how many different ways writers can construct a winning plot his second time around.
4. PWP. I like a plot, not a sexual fantasy. Enough said.
5. WIPs. One of my pet peeves is to become involved in a good story only for the writer to not complete it. I have found that the majority of stories on this site are not complete. So for the most part, unless I've found a writer who generally completes their work, I won't begin a story until it's completed. We all know that life has a way of interfering with this, jobs change, children happen, illness comes. But for the most part the authors I favor have more than two completed works which are well written and I have enjoyed them.
6. Length. A writer has to be really good to hold my attention over 300 K words. Some of these listed can do that. I also am not a fan of short one shots. I don't list some talented writers who specialize in only short stories. I enjoy some good short stories, but they are not my main fare.