What is the suggested pattern on paper to learn handwriting? What is the suggested pattern on paper to learn handwriting?
On the web, I've found many kind of paper, such as those named 九宫格 jiǔgōnggé, 米字格 mǐzìgé, 田字格 tiánzìgé, etc.
I've got a book of chinese characters in which some characters are displayed on a 九宫格 jiǔgōnggé pattern while other characters are on a 米字格 mǐzìgé pattern.
I wonder which one should be preferred (if any), or if different characters suit better on certain patterns. Which paper is used by children at school, for example?
I would suggest go ahead try them all by yourself, it vary from people to people. But same as @Stan said it is just helping you to have a better sense of positioning each stroke.

But I want to mention that it only works well if you have a sample showed in a similar pattern and you try to make it looks the same way. 

Think about what you would do to an English handwriting practice paper for English, it's actually the same idea. You need to firstly actually know where you should write on it, and then practice. And the eventual goal is no longer need it.