Two cents from a non-expert, but a great lover of "off the knuckle" shooting:
If the bow doesn't have some kind of rest on it (again, just my friendly opinion), I wouldn't put one on (though a little chunk of leather DOES work nice), and just have them enjoy the simple beauty of it all. Especially since this is for kids. What a great, straightforward and basic way to start with archery!
For sure, a modern shelf bow might have a faster learning curve, so that might be a consideration in this case... But the stuff about arrow selection being more important with non-shelf bows; while that's completely true, I don't think it's so critical for kids.
And I'd highly recomend binding (whipping) the leading edge of the fletching - just the transition of shaft to quill. Some super glue and thread is all it takes.
My 6 year old and a neighbor kid (who's a bit older and shoots with us) are both going off the knuckle now. I know he'll progress through other bows over time, but it's nice to see them experiencing that link through time/ cultures while they're still young.
But either way, your kids are lucky you are looking at wood bows for them! That's the way to go!