What is the best inexpensive camera for low light action shots?

I have recently had a baby and have been taking lots of pictures of him with my iPhone… I know… Bad. Needless to say I have missed out on a lot of great shots. Now that my baby is more active and never sits still I have an even harder time getting a good picture of him. I'm looking for a camera around $350 that is easy to use and will not produce blurry pictures. We're inside just as much as we're outside so a camera that does well in low light is a must.

Your problem is that no camera with a sensor smaller than DSLR size does well in low light, and blurry pictures are more to do with the shooter than the camera.

You MIGHT just stretch to a Canon EOS 1000D (Rebel XS) or a Nikon D3000 or D3100 with standard zoom, but just about anything else will be incapable of coping with the light levels without flash.

Check these cameras out,
http://www.bhphotovideo.com/...rtclk=sort

This is a group of point and shoot cameras featuring a 1/1.17" size sensors
Sensors slightly bigger than the common 1/2.3" found on most common point and shoot cameras
Bigger sensor meaning it can receive more light
Besides the bigger sensor, they also have faster larger lenses - f/1.8 to f/2.0 & even f/1.4 - which again translates to better low light abilities

So my pet would be the Lumix LX7, with a huge f/1.4 max.aperture
http://www.bhphotovideo.com/...amera.html
presently marked at $376

You can start using it on auto mode till such time you are able to learn some bit about photography and using the controls on your camera
eg.using it on aperture priority mode with the widest available aperture - f/1.4 in case of the LX7
some reading about the 'exposure triangle' and things like that
http://www.cambridgeincolour.com/...posure.htm
a google search will yield much reading matter

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