MediaWiki (+ a finely tuned PHP system, because mediawiki is unusably slow without it), MySQL, and plenty of time / resources for doing the large import of enwiki (since that is what most people are interested in).
Exactly, and at that point you still don't have the static HTML files. You have to crawl the entire local site, which takes ages. Then you have to repeat all of this according to your desired update frequency.