This seems like a lot. I would tend to select the ones that you are the most interested in.
Does probability have calculus as a prerequisite? You might want to wait on this one. Personally I loved probability and then later stochastic processes. However, only had one (very good) probability class as an undergrad and was into graduate school before I started taking multiple classes in this area.
What are the prerequisites for understanding weather forecasting? I am guessing that this would use a lot of math and computers but I really do not know.