The problem I have with web design software, is that it will often produce mixed results behind the scenes, even if the pages look okay when rendered in a browser. Everyone has their own way of approaching the problem; my preference is to use individual tools for each task:
For Windows I use Adobe Photoshop for raster image editing and Fireworks or Flash for vector based image editing. adobe.com/
The GIMP is another handy (free) tool for image editing. gimp-win.sourceforge.net/
Notepad++ is a useful text editor that I use for coding and markup. Lots of advanced text editing features. notepad-plus.sourceforge.net/
WYSIWYG editors like Dreamweaver aren’t bad either, but can produce unclean markup, creating accessability and maintainability issues in the long run. So it pays to have an understanding of XHTML/CSS and the philosophy of separating design (CSS) from content (XHTML) if you’re going to use it. More info about this approach to web design can be found in this article: en.wikipedia.org/wiki/Tableless_web_design. The newer versions of Dreamweaver are a lot better at generating tableless layouts, but aren’t perfect.
The XHTML/CSS validators on the W3C’s website are especially useful tools for checking your markup and stylesheets: w3.org/QA/Tools/#validators
The Firefox Web Developer extension adds a toolbar to Firefox allowing you to resize your browser to different display resolutions, and highlight different elements on the page. Good for testing and debugging issues. addons.mozilla.org/en-US/firefox/addon/60
htmldog.com is an excellent resource for XHTML/CSS tutorials, as well as a (complete?) list of tags and styles. Thanks to Scott from these forums for showing me this site
Hope that helps.