Hi addon:
A "direct-to-MP3" recorder records the audio stream directly in MP3 format (without first recording it as a WAV file, then converting it later to MP3).
My favorite MP3 recorder is EASY HI-Q RECORDER (although there are lots of other ones out there) because it is so easy to use. A freeware version (with fewer features) is also available. Download either (or both) here:
http://www.roemersoftware.com/
If your streaming downloads require only minimal editing (say maybe chopping off the head and tail of superfluous stuff), maybe this editor will work for you. I use it all the time for simple edits. It edits the MP3 file directly without converting it to a WAV file first:
MP3DIRECTCUT (freeware)
http://www.mpesch3.de/
If my download needs more help than MP3DIRECTCUT can handle, then I use WAVEPAD, which has lots more features.
I also try not to use my computer for other intensive tasks while I'm downloading, because even with a high-speed connection, I sometimes get dropouts in the audio stream I'm recording if my computer gets "busy."
Jerry