The first and most critical decision you need to make is whether a postdoctoral fellowship is necessary for the career that you desire. For most research careers, the postdoc is the de facto terminal degree. There are a number of other reasons one might want to consider a postdoctoral fellowship:
• Opportunity to learn new skills • Time to publish and write grants • Provides a competitive advantage over other candidates • Allows crossover into a new field • Time to explore new area of country or world