Some of the most commonly used and lowest cost cores are any of the several light woods. The most popular is Balsa, but substantial use has also been made of Spruce, Western Red Cedar and many others.
The reason for the popularity of Balsa is its good strength to weight ratio. When oriented in the sandwich so that the grain direction is perpendicular to the sandwich facings, its compressive strength is higher than nearly all other cores, even that of all but a few of the high-performance honeycombs.
Balsa cores suffer from having a shear strength that is not nearly as impressive as their compressive strengths, as well as from the usual wood problems of sensitivity to fungus, rot and moisture absorption. (And even Termites!) The better suppliers of balsa have a primer coat sprayed onto the faces to limit the absorption of resin into the end grain. Without the primer, you may have a lower initial cost that is later offset by a higher resin consumption, and a heavier than expected laminate. Because the material has such wide availability, reasonable cost and performance, it has been used in many commercial, industrial and marine applications.
We supply a good quality, primed balsa with all the relevant certifications in various thicknesses, contoured and on a scrim.