I self-taught myself web design and development, and I have a background in engineering. You are comfortable with computers, so you are in good shape. To get started, I took a few online courses from http://www.hwg.org/. The courses are self-paced but moderated, and you get a lot of hands-on experience right away and you get an online community to help you bounce ideas around.
I took the HTML course, almost all the CSS courses and some JavaScript. Once you get some basic experience and learn the fundamentals, you can decide how much of the other stuff you need, for example, PHP/MySQL, or whether you need some design courses to make things pretty.
I would say, you need to put in about 80 hours of practice to master the basics, so give yourself a month of self-learning to get to that point. The reason to get to that point is that you will be fluent enough to ask good questions that will get you to a higher level.
About books, go to your local library and skim through a few books, find one that you like, buy it, skim through it and skip the parts that don't appeal to you.
Finally, if you really want to learn how to build web pages, get a good text editor and hand-code your HTML and CSS. In the long run, hand-coding is more efficient and you save quite a bit of money by not buying expensive tools like Dreamweaver. However, keep in mind that tools like Dreamweaver are often used by professionals and they serve a good purpose in production environments typically found in commercial web design firms. I actually use Dreamweaver in code view where I hand code my pages, but I have a few other editors that I use depending on the project.
Best wishes as you venture forth into a new and exciting field, and remember to have fun!
