The founding fathers did not want the executive branch to be able to declare war or to engage in war without a declaration of war. They specified that the declaration was to be done by the elected officials that were more closely controlled by the citizens - the House of Representatives.
The principle, beyond the declaration of war being closer to the voters, was that the government defend our nation against foriegn aggression.
In the past, a declaration of war was always against a nation-state. Even when Jefferson finally sent our brand new navy against the Barbary pirates - middle-eastern nations were the declared enemy. ("...from 1530 to 1780 as many as 1,250,000 people were enslaved [by the Barbary pirates], they were being directed by leaders of Islamic nations." - Wikipedia)
"Congress never voted on a formal declaration of war, they did authorize the President to instruct the commanders of armed American vessels to seize all vessels and goods of the Pasha of Tripoli 'and also to cause to be done all such other acts of precaution or hostility as the state of war will justify.'" - Wikipedia.
The nations involved were Tripoli, Algiers, Tunis and the Sultanate of Morocco - but, collectively, they were the Ottoman Empire and usually acted as a single nation.
"In 1802, in response to Jefferson's request for authority to deal with the pirates, Congress passed 'An act for the protection of commerce and seamen of the United States against the Tripolitan cruisers', authorizing the President to '…employ such of the armed vessels of the United States as may be judged requisite… for protecting effectually the commerce and seamen thereof on the Atlantic Ocean, the Mediterranean and adjoining seas.' The statute authorized American ships to seize vessels belonging to the Bey of Tripoli -, with the captured property distributed to those who brought the vessels into port." - Wikipedia
The Barbary States had been taking Americans as slaves, extorting the United States government to avoid attacks on American shipping, and taking merchant ships flying the American flag.
The two principles at stake were followed: Congress authorized the war and it was to defend against attacks on Americans by foriegn actors.
The legislation we need today would declare war against those organizations engaged in acts of terrorism against the United States (ISIS, Al Queda, etc.) That each such organization would be named explicitly (obviously, it could not be left to the discretion of the administration). When new terrorist organizations spring up, Congress would amend the declaration of war to include them. And the legislation would state that any person or organization providing material aid or support to such organizations could be convicted for aiding and abetting the enemy in a time of war.