You don't need a good website logo as much as you can't have a bad one.
Good website logos aren't really noticed that much because it's assumed that it looks good or it represents your company in a fancy way. However, having a bad company logo makes your entire websote look bad because it's on every page. It's seen constantly.
The company logo show flow with the web design look and color codes. That way it won't be noticed as much, it will be passed over and just seen as good looking web design.