It's easy to integrate Wordpress into a static html site.
Integrating WordPress with Your Website « WordPress Codex. (You do need mysql, but almost every hosting company out there offers it.)
If you want to convert an existing html site to Wordpress, look at Theme Development « WordPress Codex. Developing Wordpress themes is no more complex than other CMS's, and here are lots of tutorials out there. You divide up your html into header.php, index.php, page.php, footer.php, etc., and css into style.css. If you do a standard Wordpress theme, then plugins will work fine.
Go ahead and do a full install of Wordpress; there's no option for a minimum install. WP is small, anyway.
If you need a finer degree of working with editors, subscribers and contributors than Wordpress offers out of the box, look at different plugins that offer role managing capability, giving administrators the power to give different levels of permissions to users to write, edit and publish. WordPress › Search for roles « WordPress Plugins
You can pull other content into Wordpress via RSS, too, and either have that content appear as an RSS feed, or have it integrated into published posts. FeedWordPress | simple and flexible Atom/RSS syndication for WordPress
You can get a free account at wordpress.com and try out a limited version of Wordpress, limited in that it is hosted by wordpress.com and you have a small number of plugins and css modifications you can make. But once you selfhost Wordpress, then you can do much more with it in terms of plugins and adapting the css to an existing site.