The board dimensions listed on the label at Lowes or HD are what is called the Nominal Dimensions. These are what the board measured before it was smoothed and cut to be sold. For example what is referred to as a 2x4 is actually 1 1/2 x 3 1/2 if you measure it. It was confusing to me when I started woodworking why none my plans worked out as I had sketched them.
This chart will help when you are working out plans for a project.
All the parts I listed are the nominal size. They are all readily available at your local store. I think the back piece is a 1x4.
You would need a router to make your own keyhole slot in the back or you can buy a key hole hanger at Lowes/HD and screw it to the back.
If you want the shelf to hang flush to the wall you can recess the hanger it into the back piece.
Hope this helps. Post pics when your done.