The logo doesn't need to have an orange goldfish on it, although that is an obvious choice (perhaps a black one is acceptable).
The logo needs to contain (or represent) the word 'Goldfish', and some image (eg a fish) such that the image can also be 'cut out' and used independently on it's own. An example of this can be seen at http://pivotaltracker.com, although the font, kerning, etc are completely up to the artist. It is acceptable to place the image outside the word 'Goldfish', or stylized inside it.
Goldfish is always spelled with a capital 'G' and lowercase letters afterwards.
The logo should have an alpha background so that we can later change the background color to suit the final colors of the website. The website will always use white/pale backgrounds and will never be black.
As such, no white 'edge' around the image would be accepted, unless it's a deliberate white border (eg >2 pixels thick), as this would look awful if we changed color scheme to pale blue or to pale green.
The final artwork should be supplied in a range of vector formats (eg .ai, .svg) and a range of 32-bit .png sizes.
EDIT: The image (eg a fish) needs to be energetic/edgy/wicked/vibrant/alive rather than cute/scared