Am I on the right track with this girl?

Their is this girl that I really like. We went on our second date tonight. At first I was thinking of asking her to start a relationship but thought better of it and decided to hold off. I asked myself what's wrong with being good friends with a girl for a while before moving into a relationship? It's nice actually being able to have a female friend to go out and do things with. Before I was itching of starting a relationship but now I feel just take my time and let things happen naturally. For example, first couple dates were only hugs this date was a kiss on the cheek. My question is why do people just after they meet each other start a full fledged relationship? Is this the right way of going about it? I just don't want to be all high strung and scare her off ya know.