Vectric Cut 2d would be an affordable and user friendly software program for you to use to cut signs like the one shown.
You can also download 3d models from Vector Art 3D and use their free 3D Machinist software to generate the toolpaths to cut the 3d model. You can import these toolpaths into cut 2d and cut the 3d model and also generate and cut additional 2d toolpaths for your sign.
Like James says Jarrah and Western Red Cedar would be good choices but you could also use things like the new extruded decking materials.
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