The shelves on top of the cabinets should all be connected together to make the impression of one continuous surface. They could be cut with notches for the melamine sides, but we just used little blocks to fill in those gaps. Those were glued and screwed in since they were small, and we use wood putty to fill the gaps and sanded it smooth. After painting, it looks like one continuous piece. At the sides we added the plinth blocks at the bottom, the rosettes at the top, and fluted molding on the sides. Note that these do extend into the shelf space a bit, and this is by convention and design.
The baseboard is 1"x3" pine, and the top face molding is too. Each is attached with a 1/4" reveal from the bottom and top shelves. The baseboard does not need to touch the floor (but it can) since we add shoe molding on the face.
We added crown molding to match the existing room molding - some tricky cuts where they meet, but we used the coping method to match that.
On the front edge of the shelf above the cabinets, we added some trim molding - it's 3/4" thick, so matches the front of the shelf.