What High School courses should I take to become a Software Engineer?

Ideally you’d take the most advanced math your high school offers. For most that’s Calculus AB. Some schools offer BC too. It’s really a matter of where you are now and what the sequence looks like going forward. Don’t choose finite math or statistics over the Calculus prep path.

As for science, Chemistry and Biology aren’t relevant to the types of engineering you’re interested in, but taking them in high school, especially the AP versions, might help with your admission, showing you took a rigorous path. More importantly you might be able to test out of taking them in college.

Physics really is the important one. Good luck.