I'm kind of interested in computer and just loved the idea of becoming a video game programmer like many others. But what do you need to know?

Right now I'm in the middle of a Java introductory class and hoped on moving on to a C++ intro class. Is this a good start? I'm taking these classes at my high school and I'm pretty intrested in it. I'm also in Algebra 3-4 and I think I'll go on to Pre-Calc or something like that next year. Thanks to anyone that answers. Hopefully someone who is a programmer now.