Ideally the logo should be something simple, because it gets displayed in many different places and usually pretty small. ~500x500px should be enough, and the main content should be inside a circle, because the corners are often not displayed.
A more detailed artwork is better for the bigger banner. Most communities seem to use something around 2000x1000px or so.
Not Electronics related: Banner and logo of this community?
Is there a reason why the banner and logo of this community are just the reddit logo?...