After using Bauer's "Story of the World" with three of my children for first grade, I thought I could give an opinion on the first volume.
Susan Wise Bauer uses an easier to read writing style with Vol. 1, Therefore, it is a wonderful book for a beginner reader, but an older child would find it quite childish. I never read the book to my children, but had them read it to themselves. So it was nice to have a book written at a fairly easy to read level. I would say a child who could read at a 2nd or 3rd grade level will do just fine reading the textbook themselves.
As for the activity book, it is a must have. Not only does the activity book provide questions and answers for each chapter, it gives corresponding pages to read in Kingfisher and Usborne Encyclopedias (I believe the newer publications no longer use the Kingfisher as it is no longer published), and provides a list of books for further reading. At the back of the book maps and other hands on activities are included along with short synopsis pages which the child can cut out, color and then put together to make a small book. If that wan't enough there are numerous activities to pick and a parent can find those to fit the personality and learning style of the student.
As a side, the test books are not necessary, but provide the parent with a way to verify the student's retention. Tests for the early volume consists of multiple choice, true/false, fill-in-the-blank and 1 essay. One problem I did notice with the test books is they do not always correlate with the questions and answers in the activity books. Many times the questions in the activity books would focus on a certain topic, but the student would be tested on something else. (To be fair the information is covered in the textbook.)
The reason I highly recommend the activity book is there is almost no prep time on the parents part. This is perfect for a busy parent and exactly what I needed as I have quite a few children and, thus, I needed something to keep the kids on track and also which had everything at my fingertips. Plus, the kids learned quite a bit about ancient history and also retained it as well.
If you are going to use the Story of the World text to teach history, then I would highly recommend the activity book as well.