The lowest ISO (in digital cameras) usually gives the least amount of noise and processing artifacts, so use the lowest ISO the scene allows you. In other words, go to the lowest ISO, and change only if you can't get a decent picture because it's too dark.
Shutter speed tends to be less important than aperture for most shooting situations (exceptions: action, or using a telephoto lens), so you would usually set the aperture based on the amount of depth-of-field you need for your picture. You then let the camera set the shutter speed (this is the A-priority mode).
For subjects that move fast, or lenses that magnify movement (ie, telephotos), you need a fast shutter speed to "freeze" the action. Under those circumstances, figure out what is the slowest shutter speed you need to get the result you want, set it using T-priority mode, and let the camera handle the aperture.
Now let's say you've got the ISO set to 100, and you've decided that F/8 gives you the desired depth-of-field, and using the A-mode the camera gives you a suggested shutter speed of 1/8 sec. Let's also assume you are using a focal length of 50mm on an APC camera (giving you an effective focal length of 80mm equivalent on full-frame), and you're hand-holding. Probably the slowest speed you can get away with without blurring is 1/60 sec or 1/90 sec. That is about 3 1/2 stops of exposure (1/8 to 1/16 to 1/30 to 1/60 plus another half stop to 1/90) which means you need to boost the ISO by the same amount to get the exposure you want. That would be: 100 to 200 to 400 to 800. So in this scenario, you have increased your ISO because otherwise you could not get the exposure you would need to get (f/8 at 1/60 sec with a 50mm lens on an APC camera).
Now let's say you're really not happy with the amount of digital noise you're getting at ISO 800. Then your options are to use a tripod, or to spend mucho bucks on a VR or IS lens or similar system that reduces the apparent vibrations by as much as 4 stops (according to the marketing propaganda). Then you might get away shooting 1/8 sec., and have an acceptable image. Realistically, however, your shot will still be blurry-looking as it's hard to focus when the scene is dark.