The Bureau of Labor Statistics lumps GIS Specialists in with Cartographers: Cartographers and Photogrammetrists : Occupational Outlook Handbook : U.S. Bureau of Labor Statistics
Good complement might be something like computer science or statistics. I'm really just starting to look at GIS, but from what I've seen so far it looks like GIS specialists are often expected to have technical knowledge of quantitative research methods, programming, databases, and sometimes web development.
I would recommend browsing usajobs.com or indeed.com for job postings related to geographic information systems. You'll get to see what kind of qualifications employers are looking for and how salaries correlate with skill set and experience.