You said, "I hear some funny things about how Halaal and Kosher meat is slaughtered..."
Just for your own peace of mind:
"[kosher] slaughter severs the jugular vein, carotid artery, esophagus and trachea in a single continuous cutting movement with an unserrated, sharp knife, which is intended to avoid unnecessary pain to the animal."
"The method of slaughter is a quick, deep stroke across the throat with a perfectly sharp blade with no nicks or unevenness. This method is painless, causes unconsciousness within two seconds, and is widely recognized as the most humane method of slaughter possible."