Wood for gunstocks needs to be strong, hard, resistant to splitting, of moderate weight, and to not stretch, shrink, warp, etc too much with changes in moisture. It should be easy to work with sharp tools, "standing up to the chisel". The trees must be large, and the wood should be commonly available so the gunsmith can rely on a supply and become familiar with the unique qualities of the species. Species difficult to season, susceptible to severe checking when drying, insect damage and rot while living or during seasoning were less likely to be used as stock woods in the past, though controlled environment drying opens things up a bit now. Folks like gunstocks to look pretty, in color, figure, or both. The traditional American species that fill these requirements are walnut, cherry, sugar maple, red maple.
Yellow birch, American beech, and white ash are good stock woods. Birch and beech have almost zero figure, but ash can be curly. Ash is strong but the grain is very prominent and it's difficult to carve across the annual rings.
Oaks and locust are considered too heavy, hickory too heavy and coarse and susceptible to swelling and shrinking with humidity changes. Odd species like myrtlewood and mesquite have been used for sporters but they have their unique challenges and attributes.
European walnut is probably the queen of stock woods.
Yes, lamination works well to make a stock that can be stronger and more stable than a "self" stock. Lamination was not often used before 1940's or 1950's, I think.