If I understood the question correctly,then Audacity is what you need.
You can record from a variety of sources,including Internet streams.The output can surely be ranging from .mp3 to .wav or .flac,provided you have the necessary codecs installed.
The application is in the Software Manager.
MB:MSI 770 C-45 / HD1:500 GB-->Windows / HD2:320 GB-->Mint 17 Cinnamon
CPU:AMD X4 640 3.00 GHz / RAM:4.0 GB / VGA: NVidia GeForce GT630