I've used TWiki in the past on a big project with distributed teams and liked it a lot: worked really well, had plenty of plugins,... TWiki was great. But don't you know that TWiki is dead, long live Foswiki? Reasons and chronology of events are detailed in Why this fork? on Foswiki website. So I would maybe choose Foswiki but not Twiki.
I could tell you that I use frequently TWiki, Confluence, Trac and XWiki and they are my favorite wikis. Confluence isn't free so it doesn't meet your requirements. Trac doesn't seem to have the ease of use you're looking for. For XWiki, I don't know if Java is an option. So, instead of making hypothesis, I would recommend the already suggested website: http://www.wikimatrix.org too. Just start the Choice Wizard and follow the steps to the final comparison.
While reading your question, Alfresco came in my mind. Like Drupal, Alfresco is not really a wiki, it's an Enterprise Content Management (ECM) system. But it has features you seem to be looking for, especially the integration with Office (you can open/modify/save documents from Office and share them transparently in Alfresco). Take a look at it, it's a really good and mature solution.