Bought my first smart phone ever 1.5 years ago. I now pay about 3200 yen a month. Ymobile has some very low monthly rates. Also don't be afraid to go with the unknowns like Ymobile. I think they are just under the umbrella with the big names, just a lot cheaper.
Wifi, yes, you use your home wifi, should be free. Ntt has the best service for phone service which includes your home computer for 500 yen a month. For us older folks its worth it when we run into trouble. That service allows them to connect into your computer and find the problems. Good for 2 home computers.