The Model 16 is a hunting rifle so it is light. If it has a plastic stock and you don't mind a little bit of extra weight you can remove the filler in the butt stock and add lead fishing weights or bird shot or BB's. Then epoxy them in place and let it dry.

Brakes will work on reducing recoil but nobody at the range will like you. The concussion going to the sides will drive away fellow shooters or get you a good cussing.

Since you say it's your first .308, did you buy it for hunting or target use?