What are some quotes that shows why Piggy is the best leader in the group?

From the very first chapter, readers can see that Piggy has unique problem-solving and administrative abilities that would make him an excellent leader for the boys. He is the one who says of the conch, "We can use this to call the others. Have a meeting. They'll come when they hear us." Piggy immediately begins to get all the names of the boys: "Piggy muttered the name to himself and then shouted it to Ralph, who was not interested because he was still blowing." Although Ralph initially mocks and disregards Piggy, he comes to understand Piggy's talents as being better than his own:

Only, decided Ralph as he faced the chief's seat, I can't think. Not like Piggy. Once more that evening Ralph had to adjust his values. Piggy could think. He could go step by step inside that fat head of his, only Piggy was no chief. But Piggy, for all his ludicrous body, had brains.

Here the only reason given for Piggy to not be chief is his body; he is asthmatic and heavy-set. 

When Ralph feels defeated because the "beast" is preventing them from keeping the signal fire on the mountain, Piggy suggests to move the fire to the beach, displaying "intellectual daring" not seen in any of the other boys. Piggy displays great courage and a strong sense of right and wrong when he insists that they confront Jack; he intends to say, "I don't ask you to be a sport, I'll say, not because you're strong, but because what's right's right." 

Piggy's intellect, his administrative skill, his problem solving ability, his courage, and his commitment to morality are all qualities that would make him an excellent leader for the group. Unfortunately, among the boys on the island, Piggy's asthma and physical condition made him less respected. If the boys could have respected him, he would have been the best chief of any of the boys.