Not being a cheapskate, I use primarily hardwoods. The thickness is dictated by the project. I like to use woods like Mahogany, Cherry, Maple, Walnut and exotic woods like Zebra wood, yelloheart Redheart and on and on.
again, thickness is dictated by the projects. For ornaments, I’ll use 3/16”. For plaques and wall hanging I will us 1/4”, 3/8”, 1/2” and even 3/4”. For stand up puzzles, I’ll use 3/4 - 1”.
i have a full woodshop so I am able to mill my own wood blanks, but sometimes I will purchase thin woods from my local Woodcraft store.