Because of the way Edgerank works, your posts will never reach 100% of your fans. In fact, Facebook says an average post only reaches 16% of them. That's where promoted posts and sponsored stories come in (their bread and butter).
You are dead on about being direct with your content, but the key is a careful balance. Posts that ask users to like/retweet/share certainly generate higher engagement, but if every post demands that same action, people will start to tune out. Nobody likes being forced to do something, especially in social. The real secret (which isn't really a secret) to growing your fan page is posting content that is valuable, better yet, irresistible to your audience. Do that consistently and people will share organically.
Oh, and giving away free shit never hurts