Is it legal to record songs when listening to Internet radio stations - And if yes, how is it done?

I’m thinking of buying an Internet radio using our existing WLAN. I reckon a USB connection with my PC would allow me to record songs I like. What is the best way to do this? What kind of software would allow me to take an hour worth of data and create chucks of mp3 files with the songs I like best? Can I decide about the bitrate? Or do all stations stick to a particular quality of streaming audio such as 160 kbit/s?

Another question: How many Internet radio stations are there worldwide? Who decides which are to be offered as channels of a particular Internet radio?