I agree with the previous answer that Google Analytics and the built-in Facebook stats are a great place to start for this. One question to ask is what the goals are for the business. If your goals are to increase Facebook page likes (which usually isn't a top recommendation), then your reporting will be different than if your goal is to get people to your site to order a product (a much better way to use Facebook).

It's difficult to say which key figures to use without know more about the business. The top ones are traffic, traffic sources, and conversions (if you have goals set up in Google Analytics). If you don't have enough traffic, then you need to focus on generating that, and if you are getting enough traffic but aren't converting, then you need to work on improving conversion rates. The good news is that all of this can be done with Google Analytics so long as you have it set up properly.