I could write a whole post on wood species as each species has unique characteristics and traits. But, one of the most common types of wood used in DIY projects and furniture building is pine wood (a softwood). Pine is an affordable and readily available option at your local home improvement store and it comes in many sizes. I highly recommend using pine for beginner woodworking projects. Then, as you improve your skill, try working with some different wood species!
Working on one side at a time, glue and nail the side to the back. Apply glue and drive three 1-5/8-in. nails into each shelf, attach the other side and nail those shelves into place to secure them. Clamps are helpful to hold the unit together while you’re driving nails. Center the top piece, leaving a 2-in. overhang on both sides, and glue and nail it into place. Paint or stain the unit and then drill pilot holes into the top face of each side of the unit and screw in the hooks to hold your ironing board. Mount the shelf on drywall using screw-in wall anchors.