I mostly use #8 1 1/4" and 1 1/2" square recess screws from McFeeleys and bulk buy them. I keep smaller quantities of longer fasteners as well as a few smaller ones. (#7 trim head 1" screws, for example, as I like them for certain situations)
Drywall screws "can" be used for woodworking, but they were NOT designed to handle joinery. They are thin, brittle and break easily. I stopped using them years ago when I moved to the screws I use now.