Yes, depends on them being "clickable" or not - that's why my initial response was this question.
If clicking on an inserted image has no effect, then the only version a visitor sees is the one on the post. So for best quality (and no waste of storage space) you upload and insert 656px wide images. That's because you get best quality on the post when an image is displayed in its original size: images downsized by WP lose some color and sharpness; see this post of mine for an example:
If clicking on an inserted image links to a different version of the image, then normally this would be a larger version, wouldn't it? Ideal size in this case depends on whether you link to an attachment page with the image on it or to the image file.
Attachment pages on Visual are the same as static pages with no sidebar. So if you want widest possible plus best quality on attachment pages, you upload and insert 970px wide images.
But there may be a different reason why one might want to link to attachment pages: not in order to display a larger version of the image but in order to display notes on the image. In that case I would upload 656px wide images (for best quality on the post as well as on the attachment page.)
Linking to the image file means you see the image alone in a plain browser window. So you see the image in its original size as long as its width and height don't exceed those of your screen. The problem is that screen resolutions vary (mine is 1680x1050, but that's a lot larger than average), so one cannot give precise advice in this case. I would suggest no wider than 1100px and no higher than 700px.