For writing any calligraphy, you need three things, a pen, ink, and paper.
I would reccomend just using a chisel tip marker for beginners, but if you really want to do it the real way, buy a dip pen set with nibs, holder, and ink.
You can use any type of ink (except fountain pen ink) to write calligraphy. Ex. India Ink, Chinese Stick Ink, or pigmented acrylic ink.
Use whatever you want pretty much.