You won't learn anything practical in school, just warning you now. Anything you learn will be at a conceptual level and it's up to you to figure out how to apply it. That being said, I didn't start programming outside of school until after the 3rd computer science class in the series (advanced data structures and algorithms - aka really in-depth C++). I could have, and should have started earlier, but I was overwhelmed by people in this community and thought I was way behind. The truth is that you can do all of this without any formal schooling; there are tons of tutorials and really great documentation now. Apply the effort and start now.
With that out of the way, it's not about the languages you learn. Once you learn a language, you know pretty much all of them in that paradigm (it took me like 3 days to learn C# with a C++ background). C# is one of those general-purpose languages, but there are a LOT of languages; some are better suited for certain things. The tough part is knowing when to prefer one over another.
If you REALLY want to be a great programmer, learn the concepts of a language that falls into the imperative programming paradigm (like C# or C++, although these are multi-paradigm programming languages), then go learn some languages "purely" in their paradigm (e.g. Scheme for a functional language, Smalltalk for an object-oriented language, Prolog for a logic language, etc.), then learn the concepts of assembly in-depth. Oh, and learn those pure languages by reading the published standards. Good luck.
@'Emil - Yeah that's bad advice. I'm a 5th year senior at a reputable college for computer engineering (on the computer science side, not the electrical engineering side), and IBM hires graduates straight out of school for $72000 a year + paid vacations, health care, etc. Web development would almost never have a stable guarantee of pay that high, but I ASSURE you that the web developers who do make a lot of money have experience in languages not related to web development that gave them an edge over those who didn't, so your advice is just plain wrong and bad.