To rid of noise, is it safe for me to say that we have to set it to a lower ISO? Are any factors being compromise when we set it to a lower ISO?
Some background on relationship of ISO, Aperture and Shutter Speed.
ISO
Its like an amplifier in your home HiFi system. It takes a small signal and blows it up. Similarly on your camera, light falls on your CCD/CMOS sensors and build up electrical charges, how fast this charge builds up depends on the intensity of light falling on it. Your ISO setting is an amplification to your sensor readings. The larger the ISO value the larger the amplification factor and "brighter" the captured image would be.
Aperture
Its like a window to your room, the larger you open it the more light falls into your room but light gets more dispersed. As you gradually close the window, the light rays get gradually concentrated. This parameter affects your Depth-Of-Field (DOF). Wider your aperture and more light enters, you'll get smaller the DOF a "brighter" image.
Shutter Speed
This is how long you allow light to build up the charge on the CCD/CMOS sensor. The longer the duration allowed, the more the charge builds up and the brighter the image becomes.
To increase shutter speed, you need to increase ISO, open up the aperture or both. When you lower ISO in low light conditions, you probably end up needing a longer exposure duration (slower shutter speed) and thus the inability to freeze moving subjects. However, you get images with lower noise. Although noise may still be apparant but it won't be as significant as a shot taken at high ISO. Reason for this is that noise is suppose to be random, they are distributed evenly throughout the duration of exposure. For the case of ISO, a high ISO value will amplify the readings on the sensor, not forgeting that noise would be amplified with the same factor too.
Simply to say, you want a harmony between the 3 parameters. Give and take. Hope this helps.