Well one thing's for sure, education isn't finished! There's a whole lot to learn, and the more we learn the more we seem to need to learn.
If you're really starting from having no programming background whatsoever then I think you'd be advised to take a staged approach. For example:
1). A web page with a few different text formats and pictures and colours. Here you're just learning HTML. For that any browser and a notepad editor would do, but probably a tool such as Eclipse that gives some HTML editing capability would help.
2). More adaptive HTML - stylesheets that let you change appearance without changing all the html. So that's CSS.
3). Using the above, improve your designs. There are loads of formatting tricks good web sites use and you'll need to learn those.
Note that by now we've done a lot of study and we have not actually written any programs!
4). Dynamic web pages. Now we move to the programming side, rather than just writing some HTML files write a program that delivers the HTML and in some way changes the content. Starting with something really simple such as including "today's date is ..." on the page. For that You would need to pick a server development technology such as Ruby/Rails or PHP or Java/JSP ... You'll get a lot of different advise about "best" for this.
5). Now you can start to work on accepting input from the user and doing something with it so that useful work gets done. Things such as databases start to become important.
There's a whole load more after that, JavaScript and so on. An experienced programmer can pick up this kind of stuff quite quickly, if you've never done any programming at all then you will need to be prepared to take a while before you can get to the level you probably target. I think the key is to acknowledge that a great commercial web site reflects a lot of collective wisdom and skill picked up over many years, and probably is the result of a multi-disciplinary team working together. For one person to match that is a big ask. For one person to produce something nice and useful is more practical, but still does need a lot of different skills. It's quite reasonable to specilaise in a subset of the skills. For example, good visual designers write little or no code but are highly valuable.