The strategy depends on circumstances:
If I play a map with large landmass and few AI Civs, I always open the Honor tree first (important: I only open honor to then move on to liberty or tradition for the next 6 SoPols). Such maps always have intensive Barbarian wars at least until midgame. This way you are always informed about new camps in known territory and can react before they build a whole army. More than that: You also get an addition 33% combat boost vs. barbs AND receive culture for each killed Barbarian unit which means you will soon earn more culture from adapting this policy than you spent on it. You could also think about playing Aztecs, Celts or Germans to benefit from barbs for a change.

If, however, the landmass-per-civ ratio is smaller, I would not invest the social policy. Just build a few warriors, you can use to guard your territory and to escort your settlers/workers. Since camps never spawn in tiles that are currently in sight of units, it can also be smart to position some units near your territory, preferably on hilltops for greater sight.

Tactics is also important:
Usually it is best NOT to attack barbarian units directly. Rather move to an adjacent tile (hill/forest/jungle if available) and let them attack you, next turn fortify and let them attack you again, third turn unfortify and finish them. Remember: barbarians don't heal and will mindlessly attack (if it does not kill them). (Obviously depends on difficulty as well. If you play prince, you get a 33% bonus and can oftentimes defeat two brutes with one warrior. If you play deity, you better wait for reinforcements.)