ABC-Clio American Government has entries for terrorist organizations like Al-Qaeda.  Search by keyword, but an initial search should include a number of connected articles, primary sources, and other resources on terrorism.  This database also provides context for American policy on terrorism and terrorist organizations.

ABC-Clio World at War also features international terrorist organizations.

US History In-Context features articles and primary sources.  The primary sources include full-text speeches, videos, and audio recordings of Presidential speeches on terrorism that might help to inform a debate of US policy.

Opposing Viewpoints - under Browse Issues choose Al-Qaeda or Terrorism or target a more specific example for your research like drones, torture, or US foreign relations to find evidence to support your argument on US policy.