[Tsuwabuki]

It's not just about the legal requirements or common requirements for the job. No, teaching certification is not a requirement legally, nor is it one that is very common. However, it is often mentioned as being preferred. It will open more doors and get your resume moved to the top of the stack. These are higher level jobs, and they are very competitive, so anything you do to get a leg up is smart.

Based on my experiences, and the jobs I want and what they require, I would say:

Masters, BA, Teaching Cert, TEFL Cert > Masters, Teaching Cert, BA > Masters, BA, TEFL Cert > Masters, BA > BA, TEFL Cert > BA