Maybe all I need is to get shielded cables for audio? It just dawned on me that maybe I should have mentioned this before. I've never spent the extra money on fancy cables and this could be the result. Also, is there any benefit of using either RCA or 3.5 mm over the other?
For what you are dealing with, there won't be a real difference. Many 3.5mm cables have a single ground surrounding the two signal wires. So if, for some reason, one of the two wires isn't driven, it could leak noise into the other channel. If both channels are working ok, then it will be functionally equivalent to RCA cables. If your 3.5mm cable has two separate cables then it will be absolutely equivalent. Before someone points it out, I'm ignoring situations where having an RCA input might have other implications, like the high impedance phono inputs on a audio amp.
When dealing with audio between stages (i.e from sound card to amplifier) you want to output as large a signal as practically possible from the output stage and have the sensitivity (volume or gain) as low as possible on the input. You obviously don't want to distort the output signal, but a sound card driving an audio amp should be able to run at full volume output. Ideally you control the actual volume with the last device in the chain, but if you want control of the volume from you computer, then start with the volume maxed on the sound card, and turn the amplifier volume up till it is a loud as you would ever need. Now turn down the computer volume to your normal levels.
By using the largest possible output from one device to the input of another, the signal to noise ratio is as high as possible. The noise is still there, its just quieter relative to the signal you want.