To get the lowest noise, most digital cameras work best at ISO 100 or 200, so use this setting and a tripod for best results.
You don't want to take a great image, only to find the noise unacceptable - especially if you want to try and sell your images, or get them published.
However, be very careful of camera shake if you're hand-holding your images. It's better to use higher ISO than risk camera-shake - noise is preferable to a lack of sharpness in most pictures. Even on a tripod, if it's windy or your tripod is set up on sand, don't risk low ISO as you may still get camera shake. If you have time, take one shot at high ISO and one at low, then compare the two images later by viewing at 100% zoom on your computer. Doing these comparisons for most techniques will improve your photography immensely, and make future decisions second nature, so that when you have to work quickly, you'll know what to do.
Camera shake is relative to focal length and shutter speed. Use a wide lens (10mm-35mm) and you'll be able to get away with low shutter speeds like 1/45th second. Use a longer lens like say, 200mm and 1/45th second will mean you get camera shake. So, notice the focal length before you fire the shutter. If you're using a long setting like 200mm, use a faster shutter speed like 1/250th second. To achieve the faster shutter speeds, either open up the lens aperture (so if you're on f11, open to f4), or use a higher ISO (if you're on ISO100 try ISO 400 or higher) - or do a bit of both.
As a rough guide, use a shutter speed at least as fast as the focal length of the lens - e.g. 100mm lens setting = 1/100th second, 500mm lens setting = 1/500th second. Wider lenses don't show camera shake so much.
If you have lenses (or cameras) with Image Stabilisation (also called Vibration Reduction, IBIS), do your own tests to see when camera shake starts to happen and avoid those low shutter speeds. For best results use a tripod if you can
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