I like using 1/2" Baltic Birch for drawer sides and backs. If the drawer is going to be a simple pullout within a cabinet where having the slides show is okay, I use half-blind dovetails in 3/4" solid wood fronts and a 1/4" by 1/4" rabbet in the backs that is set into a dado 1/2" from the rear of the sides. I use 1/4" BB bottoms set in a dado in all four pieces.
Where I want an overlay drawer front with half-blind dados, I cut a 1/2" deep rabbet inset to the drawer width (allowing for the slides) the full height of the front and cut the dovetails as usual. When the drawer front needs to be full thicknesss and must cover the drawer opening, built a full drawer box with 1/2" stock and add a solid wood front of the proper size.