The client would like the site colors to be black/gray/'reddish', so the logo should ideally be complementary with that color pallete (the site template background is black/gray/white).
The logo should ideally make use of a football-related graphic (such as a football, helmet, goal post, etc.) as well as something to emphasize the 'king' part of the name (crown, scepter, etc.).
The logo will potentially be used in print media, so it should also translate well from web to traditional print.
For the site design I prefer a logo that is more horizontal (wider and not as tall).
Most importantly, I'm open to most anything - if something doesn't necessarily conform with the things I've listed above, but looks really great then I'll absolutely consider it.