My strategy is this. First, I generally find that ISO 400 is good for indoors, and 100/200 is good for outdoors. I use these as my starting point.
I generally shoot Av mode, so depending on the DOF requirements, I set the aperture. Then I check the exposure to see what shutter speed is required.
Now if the shutter is too slow, I bump the ISO up until the SS is better.
As a last step, I take a few test shots, and use EC to get the histogram right (no blown highlights).
I know it sounds like lots of steps... but it only takes a few seconds with practice. My point was that ISO is the 3rd item to set in the exposure triangle. Noise isn't good, but its better than motion blur or too shallow DOF.