Mobile Games

Looking for some input for a leader board / incentive system for a new iOS puzzle game app. What are your suggestions?

I'm in the latter stages of developing my first app for iOS. It's a puzzle game and I want to add in a leader board system to encourage players to play more levels and gain more points. You get awarded points for each level you complete and bonus points for the time you complete it in. We also have daily challenges where you gain more points if you keep coming back every day to play them so I want to incentivize them to do this with a leader board. I am struggling to find the best option for a leader board system though. Facebook only offers a "friends only" leader board option whereas Game Center only offers a global option. With the Facebook option, they may not have many of their friends playing our app so it will be quite empty as well as the fact that if the players they DO invite don't play regularly the leaderboard will become a bit redundant. With the Game Center option it will just be filled with thousands of players they don't know and if you've got 300 points and see that the leader is on 5,000,000 it's not much of an incentive! Does anyone have any better ways of having a leader board system, ideally where people can play against their friends AND see how they fare globally? Are there any other cost effective leader board / incentive options we could look into?