I would like to rent a cellphone which makes phonecalls and text messages, and has a GPS function for finding our way around. Other less important options that we would consider based on price would be web browsing, email capacity and camera.Based on a sampling of the rental services available at Narita Airport:
http://www.narita-airport.jp/en/guide/service/list/svc_...
Phonecalls (at about 100 yen/min outgoing, incoming free) and messaging (both sms and mms), as well as a camera are typically standard features of a rental phone.
GPS and Web browsing are not, as they require data packages that are not usually offered.
Who will you mostly be communicating with using the rental phone? Phone numbers in Japan or phone numbers in your home country? If the latter, then you may want to consider renting a global phone in your home country instead.