At the time of writing this (shortly after I joined) I still consider myself relatively new to anime, although I have now been exposed to it for approximately 2 years now, and have watched many of them.
My first anime was Sword Art Online, which was shown to me by my sister - who had been watching for about a year or 2 before then. Even now, I still consider it my favorite, though I have since found a few that come close.
My favorite types of anime (and stories in general) include some type of love (which may include but is not exclusive to romance) but is also well rounded out in excitement and comedy levels. Not too much or too little of any of these things. I also prefer anime that are rated around PG-13. I can handle a little bit of mature tastes if I like the story well enough, but if the storyline itself is not all that great, I prefer to avoid anime with harems, excessive violence, swearing, inappropriate relationships, etc. I should also add that if it has a sad ending, I usually end up hating it, no matter how good the beginning was. That doesn't mean I can't appreciate the beginning, however I like it when stories have a happy ending and so when it doesn't, I can't give it as good a rating as I otherwise would have. Most of the time, I can't even rewatch the show - and I like to rewatch things.
Basically, I like prefer anime with a good storyline, that is appropriate for all ages, especially if there is a good mix of clean comedy, heartwarming moments, and exciting action (does not necessarily mean fighting - just any scene that keeps you on the tips of your toes wondering what will happen next). Most of my favorites might be described as "beautiful," "cute," or "heartwarming" (though there are a few exceptions).
Sorry for rambling on, but there's one more thing I'd like to add. I want give a special shoutout to Detective Conan. This is a really good anime that, despite having over 900 episodes and still airing, does not seem to get nearly as much attention as it deserves. It is one of my favorites, and I hope I can help spread awareness of this amazing anime that gets better as it goes along.
Thank you for reading to the end, and welcome to my page.