Newbie ham radio guy here. I just got my hands on an Icom R8500, and I'd like to record some signals on my pc. What's the proper way to do this, to minimize the added noise? Should I just use a 3.5mm cable to connect the REC out of the receiver to the Line In of my sound card, and then just use some recording software?
As long as you have in fact a line input and not a microphone input on your sound card, that is an appropriate connection.
If you notice hum or distortion in the recorded audio, you may need to use an audio isolation transformer. (There is no need for one unless you find it necessary.)