I think your best bet is to hook save_post and save the count for each post to a meta field. It’s not feasible to do the calculation when the back end is loaded, every post will have to be queried and sorted in memory. Likewise, doing it all in MySQL will require some significant query modification, and still then you won’t be able to remove shortcodes and markup from the numbers.
as far as the columns and sort are concerned, there are several answers here on how to do that, start with the Related questions column to the right. Also see this post by Scribu on the subject.