I'd keep giving them a grounding in myths that form the basis of all other stories, so a good book of Greek myths for children. Ditto Norse myths, Arabian Nights, Mahabarata, Bible stories etc.
Something simple and fun - like My Family and Other Animals
There are great children's classics to introduce at that age too:
The Silver Sword - Ian Serrallier (much better than Machine Gunners imo)
The Wolves of Willoughby Chase and Blackhearts in Battersea (Joan Aitken - in fact, anything by her)
Holes (absolutely brilliant) or Small Steps (the sequel) - both by Louis Sachar. Or There's a Boy in the Girls' Bathroom - despite the silly title, a really thought provoking book for that age group
Narnia Series
Inkheart or The Thief Lord - Cornelia Funke
Charlotte's Web
anything by Eoin Colfer or Philip Pullman
If they like gory stuff and aren't easily scared, the original Grimms and Hans Anderson stories are fascinating (I was more terrified than DC, reading those.)
At that age, my DC enjoyed classic poety - Old Possum's Cats - TS Eliot was a good bedtime read. So was The Rime of The Ancient Mariner and some of John Clare's and William Blake's nature poetry. Snippets of Shakespeare, like the witches' curse from Macbeth or the mechanicals play in MSND
When they're a bit older, moving onto short easy classics like The Third Man (Graham greene) of Mice and Men - Steinbeck, Christmas Carol, Jeckyl and Hyde etc. But I'd tread carefully, as lots of the shorter classics can be a bit dark emotionally and they miss so much of the point of a story, and are just left with the grim stuff.