A solid web developer needs an understanding of HTML, CSS, JavaScript, and the server-side scripting language of her choice. But still more important is a solid foundation in programming. You don't have to be an expert computer scientist, but you need to understand how to structure a program and how to solve problems in a sensible way.
Most professional web development involves database access of some sort. Teach yourself SQL, and use a real SQL -- not Access -- for the effort. You can run MySQL or Postgres on a laptop these days, and it's free.
Learn to design databases well. Learn about normal forms, and indexes, and so forth. The time you spend on that will pay off in spades.
Take a while to study up on security. Look at the security bugs that have afflicted high-profile projects and sites. (Hint: they're pretty much mostly about trusting untrustworthy data, or else relying on old out-of-date infrastructure, but the consequences include site defacement and the compromise of valuable information.)
And then, take on a charity project somewhere. You won't get turned down, and you'll cut your teeth, so to speak. Just make sure you're not storing social security numbers or something crazy like that, because charity workers are often vulnerable to social engineering attacks.
