Prefacing my answer to this question would be a couple of career guiding posts. Initially, it should be noted that what is presented here is simply my experience and different answers may vary. Accordingly, I would suggest that one should always be ready to embrace the nature of individual change and the dynamics of college upon your career choice. This is in no way meant to say that you will not become a teacher, or a primary aged teacher, but rather that opportunities and experiences might allow you to envision new images of your "professional self." I only say this out of personal experience. My goal throughout my education preparation was to teach at the university level. Then, I started working in a high school and this became my focus. After my first teaching job- Teaching Spanish to Kindergarten to Sophomores- at a K-12 Building, I became enamored with the Middle School child, and this is the age I have been teaching for the last 12 years. Experiences and opportunities help to create a new sense of professional self and one should be open to them.
In terms of having any minor or any further course of study with your Education degree, I have always believed that if you can afford in both time and money to gain more and wider academic rigor to your teaching degree, it will help expand your reach in the teaching market. There is a natural fluidity in the process of hiring in education. Administrators might be interviewing a candidate for one position and something might click, causing the administrator to match up the candidate to another post. The more opportunity you present in your own background, the greater the chance you can fit into this fluidity. Additionally, with an emphasis on "qualified" individuals under No Child Left Behind Mandates, the more qualifications you can present in your own background, the better it will be. There used to be a time when teachers could have "taken a couple of courses" in a subject area and be allowed to teach. The stress on accountability has changed this drastically, as any stakeholder can enquire about teacher qualifications. The more training and formal education one has in a subject area, the better it is. Another effect is that it allows you, as a prospective hire, greater flexibility in seeking out a teaching position.