According to the U.S. Bureau of Labor Statistics, there are many different careers for a person to pursue in homeland security, ranging from border control officers and counterterrorism specialists to chemists and emergency management professionals. Educational requirements vary from one specialty to the next; cybersecurity pros benefit from earning at least a bachelor's degree in information technology, for instance, while a border control agent would likely prefer law enforcement training. A number of schools offer general emergency management or homeland security programs, which may be a suitable choice for those who want to land a DHS career, but haven't chosen a specialty. Common homeland security courses include: emergency management, criminal justice, political science and U.S. government.
Sources:
https://www.bls.gov/careeroutlook/2006/summer/art01.pdf