Walker, Michael E
The accessible web editor really all depends on your website's requirements. If you are just building a basic web page, it would be fine to use Word to create it, and save it as a filtered web page. Another free option for building websites is KompoZer. KompoZer is a bit outdated (latest stable released in 2007), since it does not follow HTML5 standards, but again it is fine for basic websites for displaying information. Either way, if you choose to use an HTML editor, you will still need to know what is going on underneath the hood, to edit the code.
If you are wanting to get more sophisticated like a contact form, and you are not a programmer, then I too would recommend WordPress. Also, if you want interactivity on your site, such as the ability for viewers to post comments, you will want WordPress. There are two ways you can approach WordPress, depending on your requirements: wordpress.com, or download the software from wordpress.org to host yourself, based on your hosting provider. If you do not wish to pay for WordPress and hosting, and just want a free website for displaying information and allowing users to comment/you want a contact form, use wordpress.com. If you want to get fancy and build an e-commerce site, download WordPress from wordpress.org or look at your hosting provider's one-click installation options. Many hosting providers have it built in where you can perform the equivalent of a one-click installation for popular software like WordPress. It may be under something like Autoinstaller or Simple Scripts, or could be called Fantastico de Luxe.
There is plenty you can do with web design, with little or no programming though, so I would certainly recommend sticking with WordPress or an HTML editor, if your site is simple in nature, and not reflective of a web application. If it is meant to be more of an application, you may wish to see what WordPress can do still. There are thousands of existing plugins that can extend WordPress. If I wanted a contact form on a contact page, for example, I would look for an existing plugin that implemented that functionality.
There are even other content management systems like Joomla! and Drupal. In short, the sky is the limit when it comes to web design. Good luck.