Almost more importantly than which software you choose is to make sure you understand what you're trying to do with the wiki. Without some overarching conscious structure a wiki easily becomes unusable. Also (though not as crucial), it makes sense to learn some about the behavior with wikis, because it is no silver bullet:
http://www.wikipatterns.com
Then you may want to consider as an administrator what you are looking for in the wiki - there is significant difference in for example how scriptable they are, probably with twiki ending up on top (or confluence which I have little experience with). Also for example MediaWiki is completely adapted for mostly open environments, their ACL features are not that good. Another aspect is that these may be too heavy-weight and complex for what you want to do, and you should make do with a wiki like the one integrated with the trac ticketing system.