Hi Becky,
I think you can read the children's books which have both characters and pinyin at first.Pinyin will help you to know the correct sound and tone for each character. In the meantime, i am sure you will know more and more characters.
For the fun books, i recommend :《金色的鼹鼠》、《梦中的渡渡鸟》、《月光下的座头鲸》、《垂钓鱼的月亮》and《了不起的狐狸爸爸》。