Start by getting them used to carrying some of the Ten Essentials in their own packs. Ours started with 1 L camelbacks with a whistle, room for snacks, a flashlight, and poncho.
Most camp gear isn't too different from adults (sleeping pad, headlamps, camp stools, etc.) and can continue to be used as they grow.
Hammocks are a fun addition to camp. Make sure you have tree straps (2" webbing) so the trees aren't damaged. (Make your own hammock)
We do a lot of camping with our four kids. Here’s a list of must haves and our favorite products:
REI sleeping bag
Camelbak water bottle
REI flash pack
Patagonia capilene baselayer
good rain jacket
Much like adults, I think kid's gear needs to fit the kids.... My daughter received a gifted a rectangular sleeping bag from a friend of mine whose kids had outgrown it. It was quickly replaced by a warmer mummy bag designed specifically for kids as we tend to head out in the winter more than the summer, and the gifted bag was very wide on my stick figure child. His kid loved the rectangular bag.... Mine, not so much.
9 times out of 10 I'll find a "kids" version of what I'm getting myself. Example, REI's wool pants has a kids version... hers are blue mine black. We usually share a tent (Big Agnes Scout UL), we both carry REI backpacks (hers much smaller obviously). We both use Camelbak's (mine 3L, hers.... 1.5L I think?)... And so on. Where I can't find an exact match ( I wear Vasque boots, and she wears Merrell's) I usually pick them out using the same criteria.
Sorry, not an exact answer to your question, but hopefully helpful none-the-less.