HTML is not a programming language. If you're going for a big language anyway, why not start with it? There aren't really any stepping stones. Some experience with programmical logic is a benefit, which you will get in some respect from Javascript, but not HTML or XML.
Python is really easy to learn, and also a very powerful language.
But honestly, you're going to need to learn C, specifically. I would recommend C++, then when you're comfortable with it move on to C# and .NET.
Oh, and, you'll probably want much more than sophomore maths at some point. I would recommend taking every high school math course available. To work with 3D programming for example, you need to be skilled at;
- Linear algebra, vectors and matrix operations
- Rotation mathematics, coordinate systems, transformations, geometry
- Complex number arithmethic
- Calculus, especially vector calculus
- Basic physics (collision detection, movement, force, rotation, lighting)
- Basic statistics (probability, distributions, random number generation, artificial intelligence)
- Basic numerics (approximations, optimizations, solutions of linear and nonlinear equation systems)
Depending on exactly what you work with, some of the above will be more important than others, but all should be covered in any educational program leading up to the title of "Game Developer" these days.
Are you still not worried?

Worried? I'm not sure worried is the right word. I have a passion for this, it's something I really want to do with my life. I have motivation, and I know I'm intelligent enough for this field of work. I looked through my hard drive and found I still have Visual C# Express installed, so if that would truly be the one of the better places to start, I suppose I could try to start on that language. The thing is, and this may sound naive, and that may be so, but I'm not really sure what to "do" with that language at the moment. With Javascript, I knew I would be able to incorporate it into a website that I was thinking about creating, but with C#, I'm not sure what type of applications would be good to start to create once I get the basics down.
Just as far as my math skills, I was not implying I was going to stop taking math courses senior year of highschool (I don't even think you can do that), simply that I will have sufficient math courses.

I'd agree completely, but I had a freelance artist as an instructor a few months ago, and somehow he managed to maintain his "hippie" nature while doing that exact type of work. But you're right.

It will be interesting to hear what kind of project you intend to submit for a grade. Since programming is such an intense sport with little fanfare, sleep or reward (not counting Skittles). I wonder if you have chosen a field that will yield the most knowledge and the highest grade for your time investment.
I am certain you could learn any kind of programming. Generating usable code requires a broad understanding of the process. Four weeks is a very short time period to gain the knowledge required to produce an acceptable project. I do wish you the best of luck . . . =)

Build some small console applications that calculate things for you with user input. Parse a complicated file into objects that represent it well and are easily manipulated, and then manipulate the objects and write them back into the same file structure. Then solve Sudoku with a recursive brute-force algorithm. Create a GUI for your Sudoku application. Practice your modeling when you get bored. Then start building an XNA game and import your models into it and move them around and make them run into things and each other.

My opinion on learning program is that it's best to teach yourself. My high school didn't have any programming classes, so I taught myself the C Programming Language out of a really old book my mom had dating back to 1991.
I'm actually really glad I did that, the intro programming course at my college was an absolute joke. We did Java and we didn't even cover Object Oriented Programming in the whole 16 week semester.

I had already taught myself Java before I took that course anyway. I was lucky enough to get an internship as a Java developer during my senior year of high school. And I taught myself on-the-job. When I applied for the internship, I only had about 6 months of self taught C experience.
This fall I'm taking a "Programming for Science" course, which is C++ I believe. And I've never done any scientific programming so it should be interesting.

For the record, I was being completely serious. I just think all artists are hippies.
Going to a major development team/publisher to learn about how to write a physics library is like going to a major development team/publisher to learn how to write a graphics engine. Yeah, some of them do it, but by and large they just use pre-existing resources. So unless you want to learn how to call a function, you are better off avoiding a "real" game.
As for the art thing: You sound like an idealist, so let's avoid breaking your hopes and dreams just yet. That means hippie artists who teach "art", as opposed to people who brute force things to minimize (or maximize, if you are trying to advertise an engine :p) the polycounts in incredibly painful and script-heavy ways. Plus, you know, a hippie college professor is more likely to deal with a shadow.
As for what language to learn first: If you want to be an actual programmer (think Office Space, not Hackers), then learn C. And go kill yourself. You will appreciate just about everything else after that (and it will give you an advantage in that you will be used to brute forcing things and/or using nifty tricks).
If you want to make games, learn one of the languages Unity supports and then go play with that (so you can have immediate results).
Either way though, it doesn't really matter. Java was the first "real" language I learned (I don't count Pascal) and while I do still sometimes have difficulties thinking in terms of pointers, I can code C better than the vast majority of the people I know, many of which learned C++ as their first language. In fact, these days i have more problems using managed languages :p. And, since I have to use assembly on occasion, I am always grateful to use C.

I can only make a command line program in C++ so far, self taught and got the books but not the time to study. Real life been getting me busier each day.
Gundato I agree on the artist thing, most people don't know they suck too much for industrial uses. Those hippie artists need to stick to their craft fairs.

http://twitter.com/UbiKimi/status/12889644029 Ubisoft apparently accepts students.

Interesting. Taking a day or so tour of a development studio may be where I'm leaning towards.