I am currently finishing my bachelors in applied math, and computer science. Started to focus on machine learning this semester and hoping to do my capstone on it.
Minor in economics. Skip on taking extra macro classes and instead take as many econometrics and micro that you can. Economics (or another quantitative social science) is often the missing ingredient for a solid data science background. Sure physicists have good quantitative skills, but you also need to understand what the important/relevant [business] questions are to ask.
Head over to kaggle.com and participate in a few competitions. It will look good on your cv and some companies have begun to require that candidates have a "kaggle-score"
(Disclosure: written by a friend.)