Different institutions value different parts of a vita. A "publish-or-perish" institution--often a Research I university--will value, for example, your professional career in the field. A community college, on the other hand, will value your teaching record, almost regardless of what you have yet published. The following are some suggested arrangements of the categories for different presentations.
a. Research I University. Education, Awards, Publications, Teaching, Service.
b. Research, or Comprehensive University. Education, Awards, Publications, Teaching, Service.
c. Small liberal arts college. Education, Awards, Teaching, Publications, Service.
d. Community college. Education, Teaching, Awards, Publications, Service.
These are general guidelines. The best advice, however, is to look at the job ad, and see if it prioritizes the institution's needs or interests. Take this as a cue.
Other employment venues will require you to think along these lines as well. An arts administrator job will look to your administration experience. An editorial job may look at your rhetoric and composition training. You must prepare your vita accordingly. Again, use your good judgment, and ask for advice.