Thanks everyone, this has been really helpful and given me things to consider

I've taken a look at the Fire tabs again and watched a couple of videos on the parent controls and they do seem pretty robust.
A question if any of you are using parent control. I see that when using Freetime (for the little ones), it looks like it's hard to sideload ebooks in. Can you view side-loaded ebooks when just using parent controls on the regular (non-Freetime) interface, like one would have for an older child? And are they able to view PDFs added to the Fire even though those are "personal documents?"