Does it have to be wood? If you're going to paint it, HDU and PVC are less expensive, last longer, are easier to maintain, and easier to finish. You would need to cut into it with a knife to tell whether it was made of wood or not.
A quick google search will get you all the info you need. I've used CedarWorks, HDU Signs, and New England Carved Signs. They will carve them, paint them better than you can (unless you have a spray booth and an acrylic polyurethane set-up), apply gold leaf if desired, put them in a box and ship them to you for not much more than you could buy the materials for. This is the way to go unless you are like Gepetto living in the woods somewhere, and like the feel of a fine Swiss-made chisel in your calloused hands.
Ask the client whether he would prefer to kill a beautiful old-growth Western Red Cedar over using plastics made from refinery by-products that will last for years and put very little strain on the environment. The exhaust from the logging equipment will have more impact than the plastic sign.The client requested sustainable materials, so composites may not work. However, if it looks like wood that may be enough.