Notice the emphasis in this chapter about Saul's appearance. He was a handsome man. He was a head taller than everyone else. By Israel's stated desire to seek a king this sounds like a good choice. He was meant to be the man who leads them into battle. Why not the tall and handsome man who will in the eyes of Israel represent the country well.
These qualities look great on paper, but does that actually make him a good king? I think of the example from college football as we are in the season now. Sometimes kids who are big and strong with great arms who did well in high school come into college with big expectations. The problem is that sometimes they can't actually do well in the game. They look good to the eye before the game starts, but once things get going they just don't have it. (For example look at yesterdays Michigan game) On paper Saul looks like a great choice to be king. Will he actually be a good king? That will be seen only when we go from appearances to actions. What we can know for sure is that he will absolutely be no substitute for what they already had- God as their king.