Adrian Veidt is the smartest man in the world. He realized three years before killing half of New York city that the world would never reach world peace at the direction it was going with all the advances in technology and politics. He needed to strategically take all of his former teammates away from the equation. He did this because they were the only potential threat to his plan of eventual world peace.
First Veidt Taking out the Comedian; the first person to realize his goal and also the person most likely to stop him from destroying his way of life. The Comedian had this sense of truth to him because he didn't care for the conventional "all American" image. He understood that the world was a cold and cruel place. Those that understood that were the ones that would survive. The very thought of world peace destroyed his entire way of life. It was only natural that Viedt murder him first because the Comedian had the most to loose.
Second was the perfect man Jon, whom was made of pure existence. Jon was also the United States only blockade against outside countries willing to over throw them with nuclear weapons. So basically Jon represented the only block between a war, take him out and tension will arise.
Next he framed the only active member of his former team still at large, Rorschach for murder and thus taking out the person most likely to put pieces together and discover something wrong, and of coarse Rorschach did put them together. Before being framed for murder and disobeying