There are a lot of choices for web design software, I would therefore recommend choosing one that includes a content management system such as Drupal (my personal favorite), WordPress (easier to get started with, but less options later on) or Joomla (another common one, though I had problems with it).
An open source content management system is free to use, so there's no software to buy and allows you to install everything on the server (or lets you install it yourself using Fantastico if you use any host with Cpanel). It then means that still working online you can easily change the theme, add new pages, etc. and not only that, but that your clients can do the same.
Open source CMS systems like Drupal have literally 100s of modules that run e-commerce features, discussion forums, drop-down menus etc. whereas if you try Dreamweaver, you have to learn how to configure these kind of things yourself.
It's also worth learning about SEO (how to get a website to appear high in the search results).
Finally, I would recommend building some affiliate websites in the first instance for something that you're interested in. Just search for affiliate plus a keyword and you'll find something. That way, you can make some money from your site with an affiliate site and develop a portfolio, without actually having a client saying 'I want it like this, and like that, and my deadline's next week'. Alternatively offer to do websites for friends and family in the first instance.
Hope that helps!