I recently researched this as well and from what I understand Japan is very different from, say Europe where you can just buy a sim card, pop it in your unlocked phone, and you are all done.

From what I understand, Japan will not sell prepaid phones or sim cards to non Japanese citizens. The only option would be to RENT. Which yes you should be able to do at Narita.

Not sure of the cost, I think you pay for whatever the rental is upfront
and then pay for whatever airtime when you return. And it seems incoming calls are free usually.