**My strength is on before market fit and <$1M revenue phases** Formerly @Apple, Former VC-backed Startup, Marketing and Monetization for top 100 grossing iOS and Android App, Data nerd. Interested in helping you!
How much will it cost me to develop my application? Which channels should I use to acquire my customers? How much capital do I need to achieve my goals? Do I need to launch this new project under a new brand?
We'll discuss the early stage dilemma's you face so that you can move into the next phase of your project/business with confidence AND competence.
These platforms may be of interest to you... https://angel.co/ https://www.fundable.com/ https://www.startengine.com/
You can also apply for a small business loan (depending on your business). https://www.sba.gov/loanprograms
Lastly, I'd recommend that you don't do any of these things right now. Try reading these from Brian York (CEO @ Bliss and investor at Bassin Ventures) instead... https://medium.com/swlh/how-to-raise-your-first-100-000-for-first-time-founders-e9bef553b0e3 https://medium.com/@brianyork/how-to-get-endless-intro-s-to-your-startup-e822b278e956#.yzmonotc0
Gamecenter has extremely poor adoption so I would not recommend you lean on it.
Gamification services in general can be pretty hit or miss. Here are a few for your to explore. https://badgeville.com/ https://playlyfe.com/ https://www.playbasis.com/
I'd note that these type of leaderboards can often do great things to a product that is already working, but if you are creating something that doesn't already have a bunch of users who really like what you are making... it's a tough road ahead if you outsource (you need to in house the effort).
What are your ambitions? Why not sell it outright? What would your concern be?
Why not start a company? What would your concern be?
Could you do something different licence the technology out for a year? Could you do something like charge a variable cost to them to keep your upside?
The challenge with your question is that you are asking us to tell you what is right for >>you<<. Unfortunately we don't know enough about you yet to give the right answer.
When we did this for our own company we implemented in house, but we were at a high level of execution and resources (<100 employees).
If you are small I'd recommend http://www.referralcandy.com/. It's a very simple system that you can implement and the payment tiers let you get it fairly "invisible" if you so desire.