I bought my son a used 300 from a reader here on this forum. It was in superb condition and I loaded it up with public domain and Baen books for him.
For the OP's kids, what format of reader to get depends upon how much time you yourself want to use up filling up their readers. I got my son a Sony because that is what I myself have and already have books to share with him. Plus our library is a good one with plenty of scifi for him to choose from. (He's 16.)
There are lots of free books around as well as here on MR that might be appropriate for your kids. (Oz books, Lang's fairy tales, come to mind right off.) IDK if they come in Kindle-ready formats or not. I personally started w/the Sony because I wanted the most flexibility when purchasing/finding books and didn't want to be locked into one store and didn't mind spending lots of time organizing and reformatting, etc.
However, if you want them to be able to go to Amazon and buy that ONE new book that they are dying to read, in a hurry, then maybe the Kindle is the way to go. Or maybe not.
Delayed gratification and all that.