In Japan, a hanko (判子) is a personal seal in red ink representing your signature on most documents, mainly official ones. You’ll often hear hanko and inkan (印鑑) used interchangeably, but technically speaking, the cylindrical object made of wood, plastic, etc. is your hanko, and the inkan is the red seal that you make on paper using your hanko. Since a hanko is necessary to complete all of the important documents you need to fill out during the first week or so you are here, you should take care of this as soon as possible. In addition, you will probably use the hanko every time at work, as you will need to stamp your attendance in the staff book.
When you arrive, your supervisor will probably have it already made or take you to get one. But if nobody brings it up, make sure to ask about it. With the inscription/signature, your supervisor may suggest it in katakana, but you are welcome to get it in kanji if you like. Ask your fellow teachers or Japanese friends to help you find some good kanji to use. A bonus tip for those with a Chinese, Korean, Vietnamese or Japanese background and have a name from said background, using your last name as the kanji character is also a good idea.
You may also consider getting two hankos, one for home and one for work. Some schools can be pretty strict with how many hankos you can have, or even where you allowed to keep your hanko (i.e some schools prefer the office ladies to hold onto your hanko). So check with your supervisor if you are allowed to have several hankos.