Designing a sign for a restaurant , I would take the name in consideration If for example was called;"The Log Cabin Restaurant".
use a rough cut lumber, with a log cabin and framed in logs. with the 19th -18th scrolled type frame to match the outside architectural design of the building
i would think 3/4 inch thick wood , good outdoor paint (if painting ) and at least 3-4 coats of polyurethane.
Good luck with the sign , would love to see the finish results
David