Paid or not, this is due to the ability of your application. The App Engine has several Quotas and Limits . If your application remains within the boundaries, you do not need to pay on Google. But if you plan to use the application extensively, and if it will use a lot of bandwidth, processor power, disk, IO, etc., then you might think about paying money.
Business is another problem, it gives you support and reliability, as well as central development management. You can see other business details here.
You can also see this example: HOWTO: create a Facebook application with Google App Engine and Best Buy Remix .