My son and his girlfriend are expecting baby Nova in May. He asked that I build her a changing table or a toy box. I picked the the table.
The drawer setup in the plans is not clear, however I used 14" drawer slides. I mounted a small 1x2 on each side and in the middle to mount the drawer slides to. To accomodate the drawer slides, I had to reduce the width of the drawers by approximately 1/4 inch. I waited until the I was ready to install the drawers so could fit check them prior to final cut and drawer slide installation.
As for the Baskets underneath - they are Elfa baskets from the Container Store. They are mounted in with slide out trays.