If your experience is primarily with Dreamweaver, you should take some HTML and CSS tutorials and start writing your own code with a text editor. Notepad++ is a great tool for that. The problems with just using Dreamweaver are: 1) You will find some situations where you can't get the page to display exact how you want it. You need to be familiar with HTML and CSS in order to tweak it. 2) The code will be much cleaner if you write it yourself. Code generators often insert extra code that should be cleaned out. Also, you will find that after you learn HTML and CSS (which are VERY EASY to learn) it is quicker or about as fast as using a tool like Dreamweaver.
That being said, in regards to CMS, I like Joomla for a website CMS and Wordpress for a site that primarily wants to blog.
The biggest challenge with setting up websites for any CMS (Joomla and Wordpress included) is understanding templates and learning to create your own from scratch and modify others. You need to familiarize yourself with PHP or you will just become very frustrated with the whole experience!
If you really want to learn how to do things the right way and produce quality websites for your clients, this is what I would recommend for you, based on my own experience:
1. Learn HTML and CSS
3. Learn JQuery
4. Learn PHP
5. Learn about the CMS platform(s) that you want to offer your customers
The best book I've come across for Wordpress is "Professional WordPress: Design and Development" by Brad Williams, David Damstra, Hal Stern. I've never found a good book for Joomla -- just figured it out myself -- that's where you need to know the other programming languages.
Don't rush into offering a web design business until you're certain that you have the tools, knowledge, and expertise to offer a quality product. There are too many "iffy" or bad web design companies. If you start out and aren't able to provide websites that your clients are paying for, you will quickly be out of business and in addition, will have earned a negative reputation. Good luck!