Surprisingly very few bar stools from the mid-century were designed for the home. They were more likely to have been designed for cafes, pubs etc etc. The mid-century example shown is by Erik Buch and originates from Denmark.

Don't put a stool there! Find a tiny little bookshelf that will just fit in the space underneath - that way you can't tell that there's supposed to be that extra space there?!

Agree grey fabric not so practical for both the above reasons. The white ones look fine and the timber could tie in with your table and bench. But a colour could be good too. Could tie it in with accessories in your kitchen? Artwork? Depends if you're after a more sophisticated, neutral-type colour scheme, or perhaps something with a bit more character/fun. Cheaper stools that will withstand little kid treatment are ideal, and you can always update and change the look if they get wrecked and you want a more grown-up look down the track. Fabulous-looking kitchen by the way :) Enjoy your new home.

Black bar stools would look great, one or two pendants over table would look beautiful downlighting above island , this would then make a feature of your pendants above table.