Most apps are free, and apps with recurring fees are unusual, in fact I think they may be disallowed by the store terms at the moment. That's not to say it won't come in in the future, but for now you should be ok.
The only real 'recurring' charge you'd need to consider is on the data usage of an app. If you're not connecting via wifi, the data can add up and lead to you exceeding your limits (assuming you have a data plan with your provider).
It's easily solved by turning off auto updates, controlling how you connect (e.g. wifi only), etc. (something worth spending a little time learning about, as correct settings for your needs will have a dramatic impact on battery life too), just something to be aware of.
And seeing as the OP mentioned a radio station app, then Yes - using an app to listen to a radio app will consume some of the download allowed for in your monthly data package charge. While data packages are (typically) a set charge per month, up to a specified amount of data, using the radio station app will mean you'll go through your pre-paid download allowance quicker. Quicker. that is, than not using a radio station app, e.g. Angry Birds.