As to how the United States should handle terrorism, it's been doing a decent job so far. We could have helped to design a better (read: more decentralized) Afghan government, but so long as we maintain an airbase there that we'll use on al-Qaeda and the Taliban in Afghanistan and in Pakistan, we can help preserve its stability and prevent al-Qaeda from gaining another foothold. Airstrikes should be conducted on al-Qaeda terrorist cells in Yemen, Somalia, and other places, since they pose the greatest threat to America. Our current plan against ISIS - where we build a coalition of Middle Eastern forces to fight terrorism and then provide what they can't - works because it assigns the greatest responsibility to regional forces while still accomplishing our interests.
Most importantly, the root cause of terrorism is sectarian regimes and dictatorships. The policies of leaders like Assad and Gaddafi serve to inflame sectarian strife and thus provide breeding grounds for extremists. Therefore, undermining such regimes will advance the interests of counter-terrorism in the long run.