The basic search capabilities of MediaWiki (at least, the version we're running - 1.7.1) are pretty poor. I'd like to improve them with an extension, but there are a lot of options and I'd like to have a good starting point.
For what it's worth, the wiki is an internal one; we don't have the option, for example, of using the Google search extension, because it's not going to be able to crawl the wiki's contents. I need a solution that will run entirely on the wiki server.
Here are the wiki version details:
MediaWiki: 1.7.1
PHP: 5.2.8 (apache2handler)
MySQL: 4.1.21-log
What are my options?
We're using the SphinxSearch extension and it is much better than the default Mediawiki search. The extension installs directly in the Mediawiki server. SphinxSearch is only "supported" on Mediawiki 1.9+, but you may be able to shoe-horn it for testing purposes.
Aside: I would recommend you look into upgrading your Mediawiki install as well as Apache, PHP and MySQL. All versions you list (save for Apache) are out-of-date and have one or more exploits publicly available. I understand this is an internal wiki, but that affords you greater options for testing without interruption in service.
I think you need to do these things:
These days you should look at CirrusSearch. It's an ElasticSearch-powered search extension, Wikipedia is in the process of switching to it.