What should I use to design websites, Photoshop or Illustrator?
Is there a correct software or is it more a personal choice?
I disagree with Anaksunaman’s answer in regards to Photoshop. The other day we had a similar question that I answered (Organizing PSDs for developers) where I mentioned that in this evolving era, we as designers and coders must evolve with the workflow and using Photoshop is archaic and serves no purpose anymore in web design as an EFFECTIVE means of development. Its still a great tool for photo manipulation but using it to implement a website design is pointless, to me.
I will recommend (reference: What are the steps in designing a website?) that a better approach can be achieved with Illustrator especially with using artboards. Although, I’m not referring to designing the entire site in Illustrator Im talking about the wireframe and mockup. You should still design in the browser but if you design any icons they can be completed in Illustrator and exported. If you are going to be developing branding or anything print related I would surely hope that the logo you developed is in vector shape and that vector shape can be saved as an SVG for a scalable image in responsive web design. So a simple mockup or anything icon related can be exported out as SVG code and included in a XHTML document (reference: I made a map in AI, but the file size is HUGE as an svg?)
On the topic of coding I believe that Dreamweaver is pointless and wasted money and if you ask around at a few web development companies that I’ve talked to they chuckle at Dreamweaver. Its ok for new users but people that I have worked with that started using Dreamweaver relied heavily on the design preview area instead of working on the code and code completion is a bad habit for a new coder to rely on. You wont remember how to properly code if you always use code completion starting out. There are some great and powerful code editors that are free such as Notepad++, Text Wrangler (I prefer BBEDit which is paid) and Sublime Text.
So a recap to your question “Web design what to use Photoshop or Illustrator?”:
Both, image manipulation use Photoshop and Illustrator for logo, mockup, wire-framing, icons and anything that can be executed as a SVG. After your mockup is completed I would work in a code editor and develop the rest of your site.