You might look into the Example sketches in the IDE and pick a few then shop for parts.
Look at the Examples in sections 1,2,3 and 5 but skip 4 as it uses C++ Strings that he'd need to unlearn if he gets beyond simple. Really, avoid C++ Strings with Arduino.
Just with a button and blinking light sketch you can go through a whole range of "what can be a button?" projects and explore what can be a circuit as well. How many toys with conductive parts does Jr. have?
Teach him how to use a meter a step at a time and work Ohm's Law in there as well.
Start looking into childrens science books on electricity and magnetism. When I was young I used to eat up the How and Why Wonder Book series, by now there's probably even better.
Get a nice compartmented case, when I went from parts in little bags to storage I went with these:
Many starter kits come in something just about like that.
But they have a lot of choices that may suit your home better. You'll also want some bigger boxes in time.
I got the compartment boxes because it's easy to arrange parts by value, and I have a lot of those.
I have 1 for resistors, 1 for caps, and 2 for other bits. What labels I get, I put in the bottom.
Get something he can grow into if he takes off with it.
There's also Amazon, search words: arduino book kit
I've bought from them. Rock bottom prices make the shipping look high but when you see all you get it's still a bargain.
Small peeve, the chips I bought aren't painted labels on top but rather labels molded into the top. And I bought up to 20 of many different kinds! Hey, 5 shift registers for 75 cents, same with 2803's, RGB leds 5/$1, and assortments, I got a lot of parts from them over 3 orders and spent less than $100 total. I can overlook the labels, they don't stop the chips from working. Maybe I can whiteout the tops and wipe-off all but what's in the impressions.
I looked on your site for your kids Arduino book but didn't see it.
Could that be bundled with parts in a box?