There is a desperate need at secondary schools for teachers who know some computer science. Unfortunately the school syllabus is in an unsatisfactory and unsettled state at present. As a rule of thumb, plan on majoring in COSC if you want computing to be your main teaching area, and do COSC as a minor if you want computing to be your second teaching area. Talk to the adviser of studies in the Department of Computer Science as well as an adviser in the College of Education to ensure that your selection of papers is optimal. (See their Contacts page or check near the bottom of their staff list page for a list of Advisors/Facilitators for the College.)
To be employable as a games developer, you need to take COSC360 (game development), COSC342 (computer graphics) and COSC343 (artificial intelligence) as the games industry requires better AI to sell games rather than relying on improved graphics. These papers give you the background required to build a games portfolio. To improve the quality and depth of your games portfolio it would be sensible to join the Otago student chapter of the International Games Developers' Association.
Jobs in the high-profile world of animation are not easy to get, as companies often do not recruit but instead make appointments through personal connections. To be attractive to employers in this field, you would need programming skills, COSC342 (graphics), a personal portfolio giving evidence of artistic ability, and familiarity with standard packages like Photoshop.
A background in computing is useful to researchers in many fields. But what about doing research in computer science itself? A research career in computer science normally requires an academic position, for which one should prepare by doing Honours in computer science followed by a Master's degree and then a PhD degree.