For action photographs under good lighting conditions look for a camera with certain manual controls"
Shutter Priority
Aperture Priority
Program Control
Manual Control
These cameras will let you control the shutter speed.
When photographing movement, you need a faster shutter speed.
Almost all digital cameras have shutter speeds that are fast enough. Only the ones with manual controls will let YOU decide what speed to use.
Low cost cameras with manual controls do exist:
Canon A75, A510
Fujifilm A500, A510
There are about 50 more such cameras above the $220 price line.
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If you are looking to take action photos under low lighting conditions (without using flash) you are getting into high-end cameras.
For low light action shooting (without flash), you should look for a DSLR (digital single lens reflex) camera.
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