just to add on a bit. The noise is a humming sound or hissing sound in the back ground?
For the hum, like what marshall_law said, changing the 2 pin plug of the amp will help in reducing the hum due to the grounding. If not, it cud be also due to the single coil pickup (if you are using any in you guitar). If its the single coil pickup, then might have to live with it as its part of the characteristic of the single coil. If not, then invest in some noiseless single coil pickup and get a tech to do some shielding
For the hissing in the background, most often if you uses some high gain pedal its a norm to have the hiss, in a band context, it might not be obvious. Usually its only when you are playing guitar alone, you will tend to be particular with this hissing sound.
As what marshall_law said, cable will also affect the noise. Invest in some good instrument cable will reduce this problem, but not entirely as your guitar, pedals all make a part in reducing the noise.
If you still encounter the noise after changing everything(Pedals to guitar to amp to cable) then get a boss Noise suppressor and add in your chain of effect, sure to cut down on the noise
As for the CS-3, sorry bout it, imho, this pedal cannot make it. I would rather use a dod milkbox or marshall ed-1 if i really need a compressor.
And if you are really serious about compressor, then save up and get either a keeley comp or analogman bi-comp. These 2, either one, is probably the better compressor that you can get in the effect market.