This is my favourite topic, through trial and error I have mastered the art of the healthy snacks. Most important thing - children prefer variety over quantity, so it's better to prep them small snack bowls with 3-4 tiny amounts of each. Otherwise there is a constant stream of asking for say, a banana, then a bowl of blueberries, then a Babybel... so they overeat and pester too much.
So I usually keep a good stock of fruits & berries, vegetables for snacking (carrots, cucumber, cherry tomatoes), several types of nuts, several types of cheeses (cheddar, apetina white cheese cubes/feta, Babybel), some olives (green/black in salt water, not coated in oil)... so a snack can look like this:
- 3-4 strawberries, a carrot (peeled), 6-7 nuts (cashews/walnuts/pecans..)
- Blueberries, a slice of cheddar, half an apple
- 3-4 olives, cucumber slices, half a nectarine
You get the idea. Tailor variety and quantities around how hungry they are and relative to previous/next meal, some snack bowls can be more substantial.
If you bake, I'd say flapjacks and shortbread are quite enough, with the occasional sponge cake, or banana/walnut & date loaf etc.
You can incorporate flapjacks into snack bowls, just less of it.
You can make your own snack bowl rules, e.g. it should contain 1 berry, 1 fruit, 1 veg, 1 protein (cheese/nuts/boiled egg). Go wild. :)