What was Skynet's intended purpose?

According to the official novelisation for T3: Rise of the Machines, Skynet was designed to be an all-singing, all-dancing defence computer, capable of battlefield management from theatre-level right down to the granular level with single soldiers and mobile units. It was also going to perform intelligence gathering, weapons design and a host of other functions:

"Skynet: the revolutionary, artificially intelligent battlefield management network."

The video displayed a computer screen that showed the Skynet worldwide network of satellites.

"From strategic weapons to the individual soldier in the field, Skynet is able to control it all."

A model of the neural net computer chip that Cyberdyne's Miles Bennet Dyson had used as the basis for the first models of Skynet came up on the screen. It looked otherworldly. From another time or place. From what could have been an alien, nonhuman mind. Brewster thought that Dyson had been anything but an ordinary man.
Without Dyson leading the way before his tragic death, there would have been no Cyber Research Systems, and certainly no Skynet

On the screen, Boris Kuznetskov, one of the best chess players in the world, moved his white knight into a position threatening the black queen and king.
He played against a robotic arm of gleaming copper-gold metal, with finely articulated fingers. The Russian's board position appeared to be unbeatable.
"Not only can Skynet outthink the most inspired human adversary, but it designs the weapons it needs to meet its war-fighting plans.

"It is the definition of thinking outside the box." The robotic arm moved a rook from a middle rank. Suddenly the outcome of the chess match wasn't so clear. The Russian was rattled.
"During this match alone, Skynet invented twenty-six thousand one hundred twenty-three new variations of chess, and over six million new moves."
It was clear that the Russian was defeated and he knew it.
"Meanwhile, human generals are still playing a four-thousand-year-old game," the narrator said.

Skynet also functioned as a doomsday watch, providing total cover from any aggression against the US. Clearly whoever came up with that idea had never seen Dr. Strangelove

Skynet was going to assure world peace. No national leader in his or her right mind would dare attack when such an efficient, emotionless, capable system stood watch, unblinking twenty-four/seven.

Attack the U.S. or one of her allies and die. Simple. All the power of the mightiest nation on earth would be unleashed.

An unstoppable force.