I think you need to modify your design slightly.
You didn't include any dimensions, but based on the material you described, and what you have pictured that will be about 48" wide, no clue on height.
You also don't indicate what the wall you are attaching to is constructed of, so let's just assume it is a conventional, framed, drywalled home, so studs on 16" center.
You will need some horizontal pieces to hold the vertical pieces together, and to use to mount this to the wall. They should be let into the backs of the vertical pieces at some spacing that makes sense, and isn't distracting from the piece. You could paint them the same color as the wall as well to help make them less conspicuous. Or you could use some strap iron across the back to create more visual interest.