you can use audiograbber to record audio streams/signals
if its a video stream on the web then obviously if possible just save it to your hard disk
now for removing clicks/pops, hiss, noise, and restoring vinyl - i would go with sonic foundry noise reduction. its a directx plugin set and you can only use it from sound forge or other
sonic foundry products.. the settings can get tricky, read the help files for best results
ya need the demo?!