The most convenient way to communicate in Japan is definitely with a cellphone, though you may prefer a smartphone. The benefit of the smartphone is being better connected, being able to use services such as Line or Skype, and Google Maps/Apple Map for when you get lost, though it is more expensive and it is possible to get along just fine without it.
There are three main cell phone companies in Japan, Softbank, AU, and Docomo. The reason this is important is a general difference in price, and there are extra costs when calling or texting people on with a different company. For example, you will get charged a bit extra if you call someone with AU if you have a Softbank phone.
Something to note for the future is the frequency that AU iPhones run on isn’t compatible with the other 2 major Japanese mobile phone providers (Docomo or Softbank), or most mobile phone service providers overseas. You can go to an AU store in Japan and ask them to unlock your phone (“ロッククリア” “rokku kuria” in Japanese, apparently it costs a little under 3,000yen) but because AU iPhones are programmed to register the AU sim card inserted into that specific phone, by unlocking the phone you would probably only allow for a different AU sim card to be put into the phone. So even if it is unlocked it is very unlikely that a sim card of a foreign mobile phone service provider would work in the phone, and it’s also unlikely that the frequency of AU iPhones would be compatible with most overseas mobile phone service providers. If you are hoping to invest in an iPhone to use in your home country after leaving JET, it might be best to investigate Docomo and Softbank plan options, or consider getting a different type of smart phone.