Personally, I mostly leave serial books for DD to read to herself. I usually read longer or more difficult picture books to her. When DD was a fairly new reader, we really enjoyed the We Both Read books to read together. But picture books were really what we did at 3. Some of the best we heard about on here (there's a long thread of book recommendations somewhere) and many we found just browsing the library.
(Now, at 4, I mostly read chapter books a la Dahl to her, but they would have been too scary for her even a few months ago.)
