We forget that the Sorting Hat fully intended to sort Harry Potter into Slytherin. Not because he was pure-blood. Not because he wasn't brave. But the Hat must have sensed that Harry spoke Parseltongue and that his powers were stronger than Voldemort who did well for himself in Slytherin. Would he have been the same Harry Potter in Slytherin? Of course! He may not have gotten the support from Ron and Hermione to complete his tasks but there would likely have been others who had the courage to help Harry.

When Harry first entered Hogwarts, he wasn't looking for power or glory, he just wanted some friends. He certainly didn't want to be at Hogwarts surrounded by Dursley Clones. The way Draco treated Ron is the way the Dursleys treated him, giving him Dudley's old clothes and telling him he was a loser in hand-me-down clothes. He didn't want any part of that and knew that Draco and the Slytherin boys were too much like Dudley. So he asked for any house other than Slytherin.

The Sorting Hat said that if not Slytherin, then it had better be Gryffindor.