I'm category a- (used to live in Japan, but moved back to the US a couple of months ago).

I think jib71 explained it very well, but one thing to keep in mind is that no matter which method you choose, it's going to be fairly expensive to call back to the US from your cell phone. If you want to call cheaply, you're really best off using Skype or a phone card from a fixed location phone, as jib71 said.

To give you an idea of costs, from my monthly contract phone, it was about Y80/minute to call the US at off peak times (when Japan is asleep and the US is awake). I also had a prepaid Japanese cellphone for when friends came to visit, and that was even more expensive to call back to the US with. Rates from cell phone rental shops are, I imagine, even higher.

Even the rates for calling domestically (which you would have to do if you're using a phone card) are relatively speaking, fairly expensive. For example, I think I was overpaying, but my monthly contract phone was about Y40/min to call inside Japan.

Of course, you get free incoming calls, so if you can get them to call you back on your Japanese mobile number, you'd be all set.