I don't get it ? If you have noise when nothing is played then you don't need that info. Just cut out the parts that are dead air. Just use the parts your playing on and if it's a high gain then you'll have noise. Not much you can do about it. A gate will help but if you gate it too much you'll kill your sound. Do you get the same noise with a crunch/overdrive or clean sound? If not then it's the high gain your using. Also if your using single coil pickups you'll get a lot more noise than with some humbuckers. It's the nature of the beast.
Not sure why you guys are using Guitar Rig 3, GTR3, GearBox or Amplitube.
I've tried most of them out and although they work well personally I much prefer a seperate unit like a Pod, Boss GT10, Vox Tonelab or others that are even better. With those units I find them way more tweakable and much easier to use.
Dave