Is there anywhere (ideally free online) to find a wide range of reading material that is in extremely simple Chinese, the equivalent of perhaps "Fun With Dick and Jane" in English? https://books.google.se/books?id=Gg9iCgAAQBAJ&printsec=frontcover&dq=fun+with+dick+and+jane&hl=en&sa=X&ved=0ahUKEwiBoZPes5_nAhXuwMQBHYp_DL4Q6AEIKDAA#v=onepage&q=fun%20with%20dick%20and%20jane&f=false
I sometimes read essays written by Chinese children: RuiWang's 作文. They have all levels for free, starting from 一年级 (grade 1).
You can find many English novels translated into Chinese and available for purchase on JingDong or other sites. I read Matilda (玛地尔达) this way. I thought it was helpful for improving my reading speed.
You can access Chinese school textbooks for free at 电子课本网: the reading material is 语文. Again, starting from 一年级 (grade 1). [After selecting a book chapter, it looks like you need to scan a QR code, but you can just click it and it'll show you the pages.]
You can search 小学语文 online. There're a lot of Youtube materials. If you're in China, search with Baidu.
I found this one seems quite easy, with English subtitles.