I am planning on reading the Cambridge Histories series, starting with the Cambridge Ancient History working all the way up to the New Cambridge Modern History series. Is this a good strategy, and what are the pitfalls of this approach?
From my experience with the Cambridge Ancient History (mostly), I would say it's an ok strategy for the following reasons:
The 'good' :
the Cambridge Companions are reasonably short in volume, while definitely dealing with the main issues of research associated with the field of study.
they are compiled with the help of renowned, able historians
-they provide the necessary insight and further reading materials
The 'bad' :
the companions require an existing knowledge of how to read scientific historical literature. They are not designed for interested lay people to "get into history", but are designed for people who know what they are doing, but don't know about a certain topic.
Also, but this is dependent on the respective authors and depth of their special field, some knowledge in terminology of the respective subject matter might be necessary/assumed.
Hope this provided some guidance.