Fine arts would be acceptable, as long as you have specific courses in graphic design within your program of study. Visual communications might work as well, but again, make sure you have specific coursework in graphic design to supplement it. It's better to get into an actual graphic design Bachelor's program, as that will make you much more marketable when looking for a position. Getting good extracurricular experience during your college education is important too: internships, part time jobs, volunteer experience, etc. The degree alone isn't going to get you a job unless you know your programs firsthand and actually work with those programs to create examples of your work.
Check out the link to the Occupational Outlook Handbook's section on graphic designers. It's got some really good information (I put it below). Good luck!