I am continually amazed at the number of hits my profile receives since I am not an author, but since I do try to be a consistent reviewer, I guess many authors want to get a feel for who their new reviewer is. As you can see, I have been reading fanfiction on this site for an embarrassing number of years, mostly in the Harry Potter fandom (with a few forays into HP crossovers and such).
I have gone through a variety of types of stories I enjoy as you can see from my favorites list, although almost all of the stories I really like must be Harry-centric. I may review your story and enjoy it a lot, but it will not be put on my favorites list unless I feel that my children can read it. I also tend to prefer to wait until a story is finished to put in on my favorites unless it really blows me away.
My reviews are my small effort to repay authors for the time they put in to their creations and my way of saying thanks. Thus, I will usually comment on only those aspects of the story that I enjoyed or that intrigued me. Occasionally, if I can tell someone will accept a gentle correction, I might give concrit, but since I'm not a writer I don't have much of a feel for how to improve the plot, pacing, etc., in a story.