The choice doesn't really matter that much; they are all fine cameras (although the D5200 is too new to say with absolute certainty...it could have unknown problems). While all offer HD video, do not mistake them for a video camera replacement. The professional looking movies you see shot with DSLR cameras is not done with just the camera, but with lots of specialized equipment. Focusing with a DSLR can be problematic. That said, of the three, the D5200 is the only one with an articulated LCD, which is useful for shooting video.
I am into both photography (Nature, Landscape, Abstract) and filming.
Looking to get one of these bodies most likely secondhand.