If your intention is to do research or to teach, your objective should be to gain teaching or research experience. One obvious way is to acquire a Teaching Assistantship or a Research Assistantship. Not so obvious ways are to volunteer to assist a professor with research, not necessarily one in your own department, to do your own research project via independent study, to work part-time as an employee on a research project or in other ways. Teaching is possible via volunteering, conversation partners, peer tutoring, tutoring at the junior or high schools in Ann Arbor, etc. These decisions should be viewed as starting points.
Few people know exactly what they want.
Please contact them for further information. Information about job vacancies will be posted in nearly every department on a notice board. Ask the graduate or undergraduate secretary which board it is and read the vacancies to see what kind of jobs are out there and what ranges of salaries are offered. In some cases departments have a print or e-mail newsletter in which job vacancies are listed. Many departments have a library section and a bulletin board on which they post job related information and have magazines and publications which list jobs.