Personally, I would go Canon with a used 7D or 5D mark II. Sure they’re not the latest DSLRs, but by going the used route you can get much higher quality for your budget. I’ve seen used 7D bodies going on ebay lately for $450-$500. A used 7D will smoke anything in the Rebel line (T3i, T4i, whatever). I know because I had a T3i before I upgraded to a 5D2, which is still rocking just fine for my needs. I’d also recommend the Tamron 24-70 2.8 for a lens (again, used). The lens has stabilization built in (or vibration control, as Tamron calls it), which you will really need if you’re doing handheld work. Also, there are a lot of videos on youtube for making pretty darn good DIY shoulder rigs on the cheap. Grab a rode mic to mount to your camera and you’re pretty much good to go for any run and gun situation. And you may already know this, but in run and gun shooting with a DSLR you’re going to wanna keep your aperture stopped down as much as you can without cranking the ISO too high. You want a good amount of depth of field to work with, else you’ll wanna kill yourself trying to pull focus all day. Good luck.