There are actually 4 main telcom service providers in Japan, namely NTT DoCoMo, KDDI, Softbank Mobile, Y! Mobile. Although they’re major service providers, I don’t recommend them due to the expensive hidden charges.
You might want to try MVNOs, an operator that piggybacks on these 4 networks. A good example would be the 7GB data plan by Mobal for students at 4500 yen with no contract. If you don’t need that much data, the 3GB plan by Sakura Mobile works as well at 3218 yen.