1) We're not an imageboard or a -booru. So we don't need to have a huge number of images for each character. It's probably better to have one really good image than one good image and a lot of mediocre ones.
2) The image should represent the character well. This means that it should use their usual hairdo, style, etc. If a character usually wears a school uniform, but wore a bikini once, you should try to find an image of her in the uniform.
3) Generally, images should at least have the character from the waist up. A tightly cropped image of the character's head leaves out a lot, and should be avoided if there are alternatives.
4) Try not to crop the head. The hairdo is really important, so try not to crop it out.
What do you think is important in pictures? Post it as a comment here.
