Composite...if they even make it. Most are going to be vinyl these days.

I would think that tear out would be a problem in building shutters with composites. I would build them with the same woods used for porches such a Western Red Cedar, Redwood or Cypress. Rockler would be a good place to look for the tools you will need, they have a shutter building calculator on their site.

Plastic. However there are thin flimsy versions and substantial versions. Shop around.

Here's a site https://www.oldhouseguy.com/all-about-shutters/ with excellent information to get you started on properly designing your shutters before you start building them.

Thanks! This is very helpful.