Hi Eric,
I would recommend the Yoast WordPress plugin available at http://yoast.com/wordpress/. This plugin covers pretty much all the SEO issues you'll encounter in WordPress, plus there is a handy tool that will analyze important text fields in your posts to see if your articles are optimized for the keywords you're looking to rank for. This plugin won't put heading tags in the template, but I think it's worth a look.
Another consideration for WordPress is your permalink URL structure. As of WordPress 3.1.2, there is a definite performance issue when starting the permalink structure with either the category, tag, author, or postname fields. You can read more under "Structure Tags" at http://codex.wordpress.org/Using_Permalinks. I'm not sure how this affects SEO, so it'd be great to get some feedback on ranking results using different WordPress URL structures.