Hello dmccaulley,
It does strike me that they want the moon on a stick. Believe me, it's very easy to spec a website that has every single wiki, blog, forum, shopping cart, login script going ... and none of it will be used! To that end (and so you're not wasting your time!) it's important that all the features are really going to be used and supported by your system (buying stuff online instantly with a credit card is good but I want it shipped at least the next working day!)
That said, you're right that there are a number of scripts. I'm more of bespoke coder but you could try Joomla or Drupal for a start. Both are customisable. osCommerce is another that might tick some boxes.
I guess other forum members might have some ideas along the same lines.
Anyhow, good luck with it.
Regards,
David