If its anime, art and consistency attracts me, but if the story sucks, asta la vista. But there are anime whose art may not be good yet I still like 'em because of the story. In manga, if the art is developing or if it looks weird but still gives an "effect", I'd give it a go if the story's worth it. In any case, if the main character(s) is/are unlikeable (the usual reason I drop titles), I don't see any point in reading on, even if the story has a good premise.
Overall, I'd prioritize story. Next is good art, or in the very least, art I won't gag at. Awesome characters are a bonus. Heavy fanservice throws me off.
I find the plot is likely the most part for me, but the visual content is also a factor. If there's too much violence, it kinda detracts from the rest of it. Witty humor is also a factor, like what you find in Full Metal Alchemist and Dragon Drive.
I strongly believe that a well crafted story is the most important feature to any series... Ex: Last Exile Time of Eve Eden of The East Emma Victorian Romance anything made by Ghibli Studio and last but not least... Kaiba
now, these... in my opinion, are a few of the many excellent stories you must see if you ever get a chance.