With just a master's degree, I don't think you will have that much advantage over other newcomers. You are usually going to need some teaching experience, too.
Japan's teaching market is flooded with teachers and wannabes right now. It would make sense that employers take more people with better credentials, but sense doesn't always happen here. Many employers still want greenhorns fresh off the boat, and a big deciding factor is in their personality.
Your master's degree is not exactly in a field that tertiary education institutions would look for usually. They (colleges/universities) tend to go for people with degrees in such things as linguistics. But, as I wrote above, there is more to the picture. Unis generally look for teaching experience, Japanese language skill, publications, etc. Look at the FAQ stickies on the ESL Cafe (Japan forum, obviously) for more info on uni jobs if that's of interest.
Otherwise, expect to be shooting for eikaiwa or ALT jobs and work your way up from there.
At this point, I am only willing to dedicate a year to teaching English in Japan if a really good opportunity is available.
Beggars can't be choosers. Most entry level jobs here run 220,000-250,000 yen/month before deductions (some pay slightly more, and JET Program pays in the upper end with 300,000/month). Benefits vary, and many employers try to dodge legal responsibilities for copayments on health insurance. Work conditions themselves differ between eikaiwa and ALT jobs. I hope you know the differences. BTW, how would you define "a really good opportunity"?