I started to learn pinyin in primary school systematically.I may be five years old then. But I was taught some of pinyin before 5,such as the tone. Pinyin is quite important for a Chinese beginner. It can help you know more words especially to read it.All my books was the pinyin version which means every words were noted by pinyin .I can read without pingyin till 7.I started with newpapers,magazines then novels.

I would say characters.

Naturally kids learn characters first, as they can see characters on streets or in books. Pinyin was taught as a tool, to learn pronunciations of a characters or input characters from keyboard.

They are taught at the same time! Pinyin and characters.

我上托儿所的时候，是六七十年代，托儿所啥也不教，一上小学先学拼音，半学期后才开始识字，现在的幼儿园已经在教小孩识字了，有的识字还不少呢，可能也教拼音，幼儿园为了扩大招生，一切都随家长的心愿。上小学后，小学老师还要重教的。