Mostly the characters specially the female ones whether they are main or supporting

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.

character chemistry first,then story,then art.. just like Black Rock Shooter and K-On, good character chemistry there...

For me, it's the story, but if the characters appeal to me, it's like a treat. *U*

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.