Alex, I'm assuming you are referring to clothes stored in the drawers? You don't want them to "snag".
If so, go ahead and build the drawers out of any suitable material (e.g. pine, poplar, or even smooth plywood). Then sand the inside of the drawers to about 180, or even 220 grit. Finish the drawers w/ shellac. After the first coat, lightly sand w/ 320 grit, then apply at least one more coat. Drawers should be smooth enough not to snag.
If you use plywood, make sure it is a "smooth" surface, such as birch veneer, or the "sand ply" you find at some BORGs. Don't get the rougher construction ply.
HTH
Bill