I'm also aiming to be an Eikaiwa teacher, living in Kanagawa right now.
And yes, you should have as many (popular/widely respected) credentials as possible. It doesn't hurt to have them. I also suggest TOEFL/TOEIC/Eiken, because there are a lot of courses for teaching them.
For companies in Japan, it's all about the credentials and the university/college you went to; personality and actual skills come close second in my experience. Small places hire you for just being caucasian, though. This should be enough if you're going to teach as a second job, alongside IT related work. If you want to make it your main job and freelance program on the side (or something) places like AEON, Berlitz, James Eikaiwa are well-known.
http://english.oricon.co.jp/rank_english/
here's a ranking list on good Eikaiwa companies.
You could also get a teaching credential and teach at actual schools if you're okay with kids. Most English teachers for middle school are part-time and only come occasionally, unless it's a private school. (There's a separate, Japanese teacher for regular English classes) I haven't researched teaching credentials in Japan, though. One of my friends who teaches English at a middle school is with a company for that specific purpose. I forget what it's called. But he has a wife and a child on the way, his wife works too but they're moderately rich. I'd say you could make a living off of teaching English if you do things right.
I don't know if you have this link already, but
Teach at Berlitz : Berlitz Japan, Inc. this site is good. Even if you're not interested in Berlitz, it's good for reference.