In my experience job security is a direct result of your reputation and job performance in business. A critical skill is developing communication skills to clearly articulate your contributions to a companies key metrics in humble terms. It is critical to understand how your daily tasks contribute to the big picture and being able to tell that story. You will always be secure in your job in business if you can do this.
Hi Cole - congrats on your interest to learn more about careers in Business Administration and Management. There are many roles that you can go into with a Bachelor of Arts or Science in Business Administration. The first suggestion I have for you is to narrow down what are of business you have an interest in: Marketing, Finance, Human Resources, Project Management, Supply Chain Logistics, etc. There are many areas you can work in within Business Administration, and your college major should ideally focus on one of these areas.
As for job security, that's harder to say. No job is guaranteed long term. While some areas of work are highly skilled and in demand right now, like Information Security professionals, other roles always help support these roles and organizations, like HR recruiters and Finance professionals.
So give some thought of what areas of business interest you most and seek out people who are in those roles through your parents or family members, school guidance counselors and teachers, or online through Twitter and Linked In. Businesses could be local in your community or large on a global scale. They have many different roles where you could be a fit.
Good luck Cole!