RadioSure records "Internet radio stations," i.e., most of what you can tune into on your computer. It groks most stream-borne schedule and program name data, and almost always gets my fav shows right on time.
To record any/all audio that you can hear, get Audacity. It can take a bit if twiddling to get the incoming gain just right. It's also a hardy little multi-track mixer that imports/exports almost every music format.
For quick editing of the mp3s I get from these and other freeware audio products, I like Martin Pesch's mp3DirectCut. Chop, cut, copy, paste, drag, drop, and yes, from one job to another.