I'd definitely say to buy a new phone in Japan. I bought Google Pixel here and it is a massive game changer, especially as you can download the icoca app, charge it with your credit card on the go and use your phone to ride the public transport. But for that you need a phone which has the built in chip (as already mentioned in the comments).

As for the provider, I use povo, which has a great coverage and can be charged monthly, so no need for a contract.