Japanese calligraphy is an art. Japanese children (usually 3rd graders and older) practice it at school and some of them also take calligraphy classes outside of school. They purchase a basic calligraphy set at school or online. It includes the tools you need to start. They are FUDE (brush), SUMI (ink made from charcoal), SUZURI (the inkstone), HANASHI (white paper to write characters), BUNCHIN (paperweight) and SHITAJIKI (a mat to place under the white paper) etc.
As for FUDE (brush), there are two types of brushes. A thick one and a slender one. The thick one is used to write characters and the slender one is usually used when you write your name on the left side of the paper. You just need a thick one if you don’t need to write your name on the paper. You should be able to find the SUMI ink online.
Japanese people don’t use a brush to write in everyday life. Most children practice calligraphy just to be able to write neatly. It is a good way to practice the three types of strokes (“fade out”, “dead stop” and “bounce fade”), which is introduced in Course 1 Lesson 1 (Writing Points Part: 1).
I have seen some online Japanese calligraphy courses and videos on youtube.