Many systems engineers would encourage you to gain some work experience in your major first. However, many students in your situation have proven that there is value in proceeding directly to a M.S. degree in systems engineering. Some universities such as the University of Pennsylvania have started a dual degree program with a MS in Systems Engineering and an MBA in Business. You might wish to consider that possibility as well.

• Sign up for the Systems Engineering Job Bank. Post your resume to the anonymous resume bank. Search job postings and receive alerts on opportunities of interest.
• Join the chapter in the geographic region near where you live and attend meetings; bring your resume along and give it to everyone you talk to.
• Locate the INCOSE chapter in the area where you'd like to work and contact them. Ask if they've heard about any job openings. Ask if they'll distribute your resume at their next monthly meeting.
• Network with other systems engineers and demonstrate your knowledge and enthusiasm by volunteering for one of INCOSE's technical activities.
• College students should contact your college to see what internship programs and corporate partnerships they have with local businesses.
• College students should take advantage of any employment center resources including job fairs held on your campus.

It is all relevant, but you must be willing to expand your horizons to learn much more and to recognize that you will never know enough to solve everything yourself.

There are pros and cons for pursuing an undergraduate degree in systems engineering versus an undergraduate degree in another engineering discipline followed by work experience and a graduate degree in systems engineering. Most senior systems engineers would recommend the later course. If you have mathematical skills and strong interest in one of the traditional engineering disciplines, the latter approach is probably the superior course of action. Many of the concepts and techniques in systems engineering require maturity and breadth/depth in some system domain to master.
However many undergraduate students since the 1960s have proven that an undergraduate degree in systems engineering is a valuable passport to a rewarding career in engineering or business within both industry and government. Students in this latter case typically are more mature in their life experiences, social interactions, and interest in thinking of the “big picture” than are most students that enter college in traditional engineering programs. If you think you are suited to an undergraduate degree in systems engineering, be sure to seek out a program that provides a solid foundation in math, science, and fundamental engineering during the first two years. Also look for a program that provides sufficient electives and courses to concentrate in an engineering specialty area related to some domain of systems (transportation, telecommunications, computer or software engineering, chemical plants, etc.).
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Being a systems engineer requires one to be comfortable leading specialists on the frontier of every discipline. A lead systems engineer must lead engineers of all kinds, and perhaps physicians, lawyers, psychologists in the direction to satisfy the mission requirements whatever they are. Less senior systems engineers work with these people to obtain information and provide feedback. A systems engineering practitioner is the glue (the requirements manager, the design architect, and the one who is willing to understand the life-cycle implications) that holds the project together.

The choice of an academic program in which to enroll is a personal choice. However, INCOSE has put together an academic program directory listing undergraduate, graduate, and certificate programs in systems engineering.

Check out the Membership Types section for that information.

Yes. The systems engineering discipline grew out of many of the engineering disciplines. Many systems include a wide range of components made of hardware and software, as well as facilities and people. What you must learn is problem definition, systematic thinking, working with people from many specialties (some of which will not be engineering), and integrating ideas and concepts across disciplines. You will find yourself leaving much of the focused mathematical topics (Transforms and Maxwells Equations), but you can always go back to them if necessary.