Hi jamaljan – for high
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Hi jamaljan – for high quality video, fast autofocus and good low light performance with a $1000 budget, I would get a Panasonic DMC-FZ1000 superzoom instead of a traditional camcorder.
This camera records video at 3840×2160 "4K" Ultra High Definition (UHD) resolution – 4 times the resolution of a 1920×1080 "High Definition" camcorder.
It also has a 1" sensor – 8 times the size of the sensor in a traditional 1/3" sensor camcorder. The larger sensor gathers more light, which means better low light performance.
Here is a recording of children singing indoors at 4K (please watch at your monitor's highest resolution):
Here is the camera recording at 4K resolution in the hands of a professional videographer:
The camera can also record 1080p HD video at 120fps for slow motion:
And a Panasonic DMC-FZ1000 bundle with an SD card and camera case costs less than $900, so it's well below your $1000 budget limit.
Hope this is helpful and good luck!
Bill