Resources for complexity results for optimization problems in restricted graph classes
Get Spinrad's book on efficient graph representations:
http://www.amazon.com/Efficient-Representations-Fields-Institute-Monographs/dp/0821828150

Also check out Li and Vitanyai's book on Kolmogorov Complexity:
http://www.amazon.com/Efficient-Representations-Fields-Institute-Monographs/dp/0821828150

You will get an appriciation for each graph class by studying succinct data structures.  When you understand why certain classes of graphs take less storage than others you gain a great understanding of how to tailor optimization problems on to them.