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the most important difference between the three different types is the price and the distance to the object you are going to photograph.
If you try to take photos of small animals (like insects) there is a chance that the animals feel disturbed and disappear. With a longer focal lenght (100 or 180mm) the chance is much bigger to get a good pic.
A long focal lenght is also good to get a blurry background.
60mm is perfect for reproductions (if you do not use a scanner).
Thanks for your reply, a longer focal length sounds like it may suit my purposes, I don't want to scare those bugs. When you say the 60 is good for reproduction does that mean it is sharper than the 100 or 180? Do I need a tripod for the 100 ?
no, the sharpness is the same, only the depht of field differs. The most important difference is the angle of view. For photographing insects or small flowers, the 100 mm lens is a good choice.
A tripod is always good to achieve full sharpness. The only problem left is the movement of the objects themselves. Some people try small apertures like 11 or 16 and add flashlight, but that often causes dark backgrounds. It is a game of trial and error to find the best combination.