D5200 seems to have the best low light with 18-105mm at $999, T4i with 18-135mm at $799, or the sony A57, it has peak focusing at only $520 with stock lens 18-55mm. Will be used mostly for video and some photography.
Just like in photography, think about the system as a whole...as in additional lenses down the line. That being said, I think the D5200 is the best one for video at the moment...the new toshiba sensor and processing have given the D5200 and D7100 great video with very little moire/aliasing that will be present on the t4i and A57.
Also the HDMI out on the D5200 will allow you to record a clean 1080 signal to a Ninja or other device placing the files in a more robust and edit friendly format. I personally would buy the D5200 body only and get a couple of the inexpensive G 1.8 primes and/or a Tamron 2.8 17-50 zoom or similar 2.8 Sigma.
