You didn't say whether the goal is fundamental knowledge or employability. :-)

Splitting the difference, I'd say:

1) A Lisp or Lisp-like language. Either Racket or Clojure would be an excellent choice here; Racket is especially designed for teaching, and there is a lot of top-quality educational material for it. Clojure is probably more employable but isn't specifically designed for beginners. Recommended book: How to Design Programs, by Felleisen, et al (free online). If you want to go old-school, try Structure and Interpretation of Computer Programs by Abelson, Sussman, and Sussman. The video lectures for that one are also quite valuable.

2) C. K&R is short and information-dense. If you're going to use C professionally, you'll want more, but K&R is definitely enough for a good overview. Recommended book: The C Programming Language, by Kernighan and Ritchie (reasonably priced).

3) Maybe an assembly language. Or maybe not. If the goal is to understand computers at the most fundamental level, you might as well study the theory of computation rather than learning the quirks of a particular machine's instruction set. Recommended book: Elements of the Theory of Computation, Lewis and Papadimitriou (spendy).

4) The Javascript/HTML/CSS hodgepodge. Not anyone's choice for the greatest language ecosystem in the world, but probably the most employable one. Recommended book: sorry, I've never seen one that's completely satisfactory. On the other hand, there's probably more free educational material on the web for this than for anything else. On the gripping hand, a lot of it sucks.

5) An algorithms text. Many would recommend Introduction to Algorithms by Cormen, et al (often called "CLR" or "CLRS" for recent editions, but that can be tough sledding for a beginner. I would instead recommend any of the Algorithms in "X" books by Robert Sedgewick (where "X" is some programming language, such as C, Java, etc.). Having concrete code examples can be useful for a beginner, IMO. Once you have a handle on the basic ideas, The Art of Computer Programming by Donald Knuth is a reference you can return to time and again for the rest of your career.

5) Enough database theory and SQL to feel comfortable writing basic queries. Maybe Database System Concepts by Silberschatz, et al for the theory and one of the "SQL cookbook" texts for practical applications. Make sure that whatever cookbook you use covers things like SQL injection and that you fully understand that coverage. :-)

6) Prolog. The classic here is Programming in Prolog, by Clocksin and Mellish. However, I haven't been keeping up with Prolog for a long time. Someone else may have a better suggestion.

7) Machine learning and neural nets. No suggestion here -- it's not my field and it's been advancing very rapidly of late. Again, someone else may have a better suggestion.

8) Graphics. I like Computer Animation: Algorithms and Techniques by Rick Parent. Also, Computer Graphics: Principles and Practice by some combination of Hughes, Foley, van Dam, et al. This is a more in-depth text (actually, it's a good reference book). In either case, you'll need a good background in linear algebra and probably some calculus before tackling this. Owning both of these would be good if you're going to get into graphics in a serious way.

9) Erlang. Programming Erlang by Joe Armstrong.