I also have the expedit shelf from ikea (4x4), with the clear-ish (sort of opaque) plastic containers. I taped pictures of the toys to the inside of each bin to help the kids clean up efficiently. It works pretty well for us.

I have a lot of Melissa and Doug board puzzles, but we keep all the puzzles in zippered laundry bags (the mesh ones you'd use for delicates) to keep all of the pieces together. Our play kitchen has lots of dishes and food to clean up at the end of it, but I think that's unavoidable. One of the bins in the shelf is dedicated to kitchen stuff.

I also have a dedicated block room that is divided by a long baby gate to keep the youngest from knocking over everyone's towers. It helps them keep the blocks in one area, too, as it's sort of self contained.