From the sound of it, they want something that runs itself, with end-users maintaining content. IMO that never works. When everyone can post content, and no one actively maintains it, you end up with an unusable hairball. Someone has to have a primary mission of maintaining and pruning the site or it's little better than a shared network drive.
The easiest way to get what you want probably would be SharePoint, but turn off nearly everything. Don't give admin rights to anyone. Lock it down as much as possible, with only a very few limited ways to post content. You can get the Outlook and Project integration pretty easily ... assuming you can get it set up correctly the first time. Doing this is apparently harder than it sounds, because I've used it three different places and it never worked right out of the gate.
My personal preference is a Wiki, but when your office is MS Office document-centric you probably have to view supporting those as your primary goal. And I haven't seen anything other than SharePoint that does Outlook and Project integration.