Best bet would be a Canon semi-pro or Pro DSLR Body. They have the widest option in lenses and work Great both for stills and video. Canon is by far the best for video (with black magic hack installed)
I speak out of experience. working with proffesional grade cameras, etc..
I mainly use it for video. think i got my Canon 7D with a 70-200mm L for 700-750ish usd then spent around 1300usd on the 24-70mm. and i can say im never going to switch brand. way superior image quality and glass
(My current setup)