I love using Audacity to record streams off of the internet. I used it for years on Windows XP & may have had to play around with it a bit, but it was well worth it.
When I got a new laptop, however, I had issues trying to get it to work again. I think Microsoft changed things around a bit, I think some felt they were deliberately trying to make it difficult/impossible to record streams directly. But I did eventually get it to work with Windows 8.0 & after the 8.1 update.
I don’t know if your issues are related to the ones I had to overcome, perhaps not, as I couldn’t get the “stereo mix” option to show on the drop down list. Once that showed up, I was good to go.
Here’s a link to page two of the thread here where I was trying to figure it out: Missing stereo mix in Windows Pro 64bit - Windows - Audacity Forum
Here’s a link to the post where I described what I did to get that stereo mix option to show up in Windows 8:
Here’s a link to a post by kozikowski about a Behringer UCA 202 which I eventually did purchase so that I could also record from a stereo system. It may be an option for that loop that they’re talking about, where you plug your audio out into the Behringer & then back into your computer via a USB port:
Hopefully I’m not confusing things more than helping. I’m just a novice myself, but maybe there’s something in all of that that might be helpful.