In reply to:
You talk about DH "having" MediaWiki 1.8.2... does that mean that to create a wiki here I won't have to (or can't even) do my own installation... but can create my site's own wiki using their installation?
"Yes", it means you won't have to do your own installation because you can create your site's own wiki using the Dreamhost installation. You *can* also do your own installation if you prefer (which is how I generally do these installations).
Using Dreamhost's "one-click" installer is "dead simple", just follow the prompts on the presented screens and you should be good 
More information on MediaWiki on Dreamhost is available here, and you might find this helpful reading even if you choose to use the "one-click" installer. Make sure to note that different version of PHP and MediaWiki are discussed in this article, so remember that PHP5 is required for the "one-click" installation, and any version of MediaWiki that is 1.7.1 or higher , should you choose to install it yourself 
--rlparker