My family orders some items from this company from time to time, and I recommend it highly. You can get basic necessities like soy sauce, miso, and dashi in addition to a ton of other basics. The products are great quality. The staff at Aji to Kokoro is friendly, and the products come nearly as quickly as if you had bought them yourself at a supermarket. We ordered some things yesterday afternoon, and they were delivered at around 10 am this morning. There is also a beautifully hand written, yes, hand penned letter in the box saying thank you for buying and some seasonal message.
This is a company I would recommend to anyone living in Japan.