Wiki -- free collaboration (If you can choose)

So many wiki (or is it "wikis") so little time.. I am trying to evaluate the mass of wiki's described at www.wikimatrix.org. The site contains a terrific comparison utility that I can match almost side-by-side with my requirements.

In short, I'm looking for an online collaborative writing experience for students to contribute to a group "understanding" of a topic and use for brainstorming. The site must be able to limit who can read or edit posts, as well as provide an easy way to audit who is posting.

So far, the one that matches the closest is mediawiki. Going to try to evaluate it on siteground.com, by far the cheapest Linux-based wiki host I've found.

For $5 a month, I might as well try 3 or 4 wiki products...