We used a combination of dresser & closet, with a 2nd (lower) bar in the closet and some hanging shelves (closet organizer) that left stuff visible. I don't think kids are much better with hangers than with drawers/folding.
What does help, I think, is a set of drawer organizers. I've also used shoe boxes. Dividing drawers make things easier to keep stuff straight. So if underpants go in shoebox 1, and undershirts in shoebox 2, and socks in #3, it makes finding things easier. Do the same with a shirt drawer - organize by color (whites in one, pastels in another, darks in a third) or whatever other criteria work for you. I'd make a separate category for outfits - where tops and bottoms match. As the kids grow, shoeboxes don't work but larger boxes do.
I think kids do have to be responsible for organizing some of their stuff, particularly if they pull it all out to find one particular thing. But setting up some guidelines and organization is fine. For kids too young to read, it's often helpful to put a photo of the category on the outside of the drawer so they know where to start.