I am trying to develop a logo from this image.

The logo will be used in a variety of media, including large banners. Therefore, I assume a bitmap is not appropriate as final art because it can't be scaled up. Or can it? Is there a way to scale up bitmaps without having big-ass jaggies?

So I was thinking of importing the bitmap into Illustrator and turning the image into vectors as much as possible (using whatever command that is that draws lines along bitmap contours). However, I am a complete novice at Illustrator and am not looking forward to doing this.

Can anyone suggest a better way?