I wouldn't really worry about Google having their 'fingers in your pockets'. They're already basically filling you pockets, when it comes to traffic! If you're unsure of how to use Google Analytics, you can subscribe to this Google Analytics tutorial
I have heard GA is free but what exactly do they mean when they have this on their site before you actually sign up? (5M pageview cap per month for non AdWords advertisers.) If hit the cap, what they wont track no more til the next month or will they start to charge you something.