When is it best to use: DreamWeaver vs. WordPress Templates vs. Drupal or some other program to create websites?
You can learn any or all three and put out an effective website.I would look at what the website will need:
Dreamweaver can be used to design all three types of sites - ie, you could build a Drupal site in Dreamweaver or a WordPress site in Dreamweaver. In fact, I've done all three - Drupal, WordPress, and straight HTML in Dreamweaver.
Drupal is a CMS - so if you're building a site that needs a lot of management or is going to have people managing the content who don't know or don't want to learn HTML, this might be a good choice. Drupal offers lots of plugins and extensions like a blog, calendar, and forum. So if you think the site is going to have all those things eventually this might be a good choice.
WordPress is first and foremost a blogging tool. Yes, lots of people are starting to use it to manage their entire site, but most of the time you can tell these sites because they look like blogs. They might have 1 or 2 static pages, but typically the blog is the most important part of a WordPress site. If that's what your site is, then this is a good solution.
Finally, Dreamweaver alone. You can build any type of site you want using just Dreamweaver. You won't have the built-in tools for blogging or CMS like you do with Drupal and WordPress, but you have the flexibility to build anything you like. And as I said before, you can use Dreamweaver to build and maintain the templates for your Drupal or WordPress sites.