Hi Oliver,
Your simplest option would be to create a website in Dreamweaver and have the shopping cart as a separate area of the site, linked in via the menu. e.g. domainname.com/shop (or shop.domainname.com). You can skin it to look like the rest of your website, re-using your CSS in the same way as you'd edit a Wordpress or Texpattern skin.
Shopping cart wise, it depends on your needs. I'd recommend Magento as it's probably the most
SEO friendly system out there. Zencart's also a safe bet as it's pretty easy to style and there's a big community behind it, which is important if you're using free software.
Don't try to do anything too complex as there are a lot of factors involved in an e-commerce site. Payment gateways and stock management systems can be a real pain to code from scratch.
Hope this helps.