It's no different than the way your CD player is connected to your tuner, or the way any other standard audio components are connected together. You need balanced signals for low level sources that are going to see a lot of gain, like all microphones, or high impedance sources, like a great many microphones, or when you are going to be covering very long distances with any kind of signal, like in a PA snake, or when the signal source is powered by a different AC circuit with potentially a different ground reference, again like in a PA snake (decent gear won't be sensitive to this, but a lot of stuff most of use can be). Your computer's output is a low impedance line level source (in other words, a robust source), and you're only going a few feet, and presumably your monitors are plugged into the wall in the same vicinity as your computer. In this application, decent shielded RCA cables are absolutely all you need. (They're pretty much all going to be shielded, so when I say decent, I mean anything other than the freebies that come in the box when you buy any kind of audio gear, although to be honest, I have even a few of those in my setup with no issues). The only thing you need to watch out for is to make sure you don't run any of your audio cables right alongside a power cord or the cord going up to your monitor. They don't need to be very far apart, just not laying right next to each other. Audio cables running right next to each other is fine whether balanced or unbalanced.
Radio shack . . . 1/8" stereo to dual RCA and two RCA cables . . . good to go! It's not a shortcut or a settling for less. It's the very reason your monitors even HAVE RCA inputs. The other name for RCA cables, BTW, is "Audio" cables. There's a reason for that!
Yes, TRS would be less sensitive to noise, but zero times zero is zero. You will absolutely not have noise problems with RCA cables in this application. If you pick up noise from cell towers on a six foot RCA cable running a line level signal, or even a 20 foot RCA cable, worry about your health, not your sound, cause you're living in a microwave oven!
Now get 'er done so you can get on to more important things!
J
PS - Your cell PHONE definitely WILL make noises in your monitors. If it's close enough the monitor, it will do that even when the monitors aren't plugged in!!! I really don't know whether this noise gets into the input side of things or whether it's just the cell phone signal interacting directly with the speaker coil, but as a general rule, I don't think you want cell phones near any of your equipment while you are recording.
PPS - Don't misunderstand my comments as being in any way anti-TRS or anti-balanced signals. That would be retarded. Balanced signals are less sensitive to noise. That's an absolute fact. If your question were: "I have TRS outputs and TRS inputs and I have RCA outputs and RCA inputs, which should I use?" Obviously you'd use the TRS. And in some applications if you said, "I only have RCA", I'd say, "Well, then your going to have a problem." In some cases, I'd say get an RCA to TRS cable (which would turn a single ended output signal into a balanced signal as long as the destination device actually handles it that way. In this situation, though, RCA on both ends is going to be 100% good.
