In the first three years of the grammar stage especially, children need to learn the Bible stories in their historical context and as part of the plan of God as mentioned. The best way for children to become thoroughly familiar with them is by hearing them over and over again. If they are exposed to them enough, they will learn them because of that exposure naturally. It helps to read through the Bible in chronological order. It drives home the historicity of the Word of God, and God's perfect plan.
Children can also begin memorizing Scripture from toddlerhood right through high school.
One effective way of memorizing for small children is suggested in The Book of Life . Even little children can memorize that quickly. Almost any verse can be memorized easily in stages like this. And finally, they can memorize long passages and whole chapters. My church college-group leader practiced memorizing whole books of the Bible.