If there were a sole factor into my decision for ATOY, it would be the story since I don't get too attached to a lot of characters ...

Good characterization isn't hard when there are tons of deep characters but the same can't be said for the premise or the plot ...

Very rarely do I think highly of an anime with thin plot ...

For me is
The most important.
Story+characters+OST.
the least important.
fanservice+animation.

hmmm I guess I'll rank this. 

1. Characters. This is a make it or break it for me. If the characters are boring, irritating or just meh, I'll drop/highly dislike an anime. I'll overlook almost everything for good characters.

2. Animation Quality. It needs to be alright or better. If it's bad, cheap or looks like something an american made (southpark, family guy, archer), I'll lose interest quickly

3. Story. it doesn't need to be complex but it does need to make some sense and not have gaping holes in the plot/lore. 

4. Level of action or activity. I like some SOL stuff but if an anime is slower than a snail, I lose interest.

5. Fan service. I'm more or less neutral to an anime having it or not but if it's there, don't censor it. I hate censored anime.

6. Romance. I actually would rank this higher but I basically give anime a pass on this. Most relationships in anime, don't ever progress to anywhere behind flirting or hining at something being there. i don't take any romantic connections between characters seriously.

7. Uniqueness. This a odd duck for me. Most of the time, i could care less about it but then there's times it makes all the difference in a anime. i was completely caught off guard by Oreimo. I just enjoyed how messed up it was and I had a blast showing that anime to people. 

8. Music. It's cool when I like the music but most of the time, I don't or I don't pay much attention to it. So it's not important to me. Oddly, I like Your Lie In April. 

9. Voice acting. meh I don't really care. I watch everything with subtitles. It could change though in the future. I want to learn japanese. 

I hope you realize that what you're basically asking is if people are Type A or B Otaku.

Type B for life! *obscure gang sign*

Do I have a neon sign on my head that says "google"?

http://www.japanator.com/what-kind-of-otaku-are-you--13120.phtml

Type C is the casual. Doesn't watch enough anime to be counted.

Um no... Nagisa vs Karma fight (last ep of assclass) has something to say about that

Damn right he did. Also best girl was climbing mountains in the beginning ;)

Watched Dagashi Kashi. Very enjoyable SoL anime with lots of cool facts.

Now watching Dimension W.

Yeah it feels decidedly average at everything it does so far.