I agree with KYJon concerning gun stock grading, grain flow, etc. What he said about people making the mistake of buying flash and neglecting to think about function is so true. The articles by Pete Hiatt in the "Other Useful Information" section of this site are a very good place to start too. A couple hours with Cecil, if he has that much time, would fill your brain and give sensory overload. The answer to your question is not cut-and-dried (no pun intended), because the subject is huge. As with many things, there is also a lot of misinformation to sort through.
Going from memory, I believe it was David L. Westbrook's book "Professional Stockmaking: Through The Eyes Of a Stockmaker" that had a pretty good accounting of most all commonly used gun stock woods, and descriptions of their attributes such as grain, figure, density, stability, ease of carving, ease of checkering, and overall suitability. But even if you confine your interest to Walnut alone, prepare to spend many many hours learning about the differences between species, subspecies, and cultivars, and the great number of variations found even within different trees of the same species... or even different parts of the same tree! It's a fascinating subject though, and very useful to be able to avoid spending a lot of money on wood that may not be well suited for gun stocks.