If you are looking to shoot kids, I suggest getting a camera with following characteristics:
- fast shooting rate
- fast auto focus and able to follow kids movement
For the above points alone, I suggest getting the NEX series.
Not only it has the fastest shooting rate (10fps if I am not mistaken) for its class it is also more affordable than the high end m4/3 cameras.
It should be enough for your use, DSLR would be too much.
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Matt Mulyadi - Photoblog -
NEX is nice too, but 10fps is really not necessary for kids.
Esp. so when its many shots and most are not focused since AF cannot keep up.
m4/3 AF as of 2011 released cameras are all faster than NEX too. (ie. G3; GX1; EPL3; EP3; EPM1)
Neither are they expensive. G3 is only ~$700 body only.
Coupled with the fast primes at 12/2; 14/2.5; 25/1.4; 20/1.7 and 45/1.8, 45/2.8 macro, m4/3 has really come of age.
Very good portability and performance.