Cheap DSLR

Try asking a professional at a camera store. Then try at least two other stores. get their recommendations, go home and google the shit out of those cameras. Learn as much as you can about filming and DSLRs... Then come back here with choice if you want to ask NS.

My 2 cents. DSLRs out now can do a decent bit at recording video. Generally the newer the camera the better technology and better results but you will be spending more money. Video has been developed into DSLR sensors for quite some time now so the bugs are out and the cameras are on a pretty decent playing field. The biggest jump recently has been mirror less cameras and super high ISOs. Super high ISOs (check out sony) you do NOT need on the ski hill but you will LOVE if filming at night.
Lots of shutter bugs (photographers) are always in the hunt for the latest and greatest so they sell off their recently "outdated" camera body and get the next one. Look for those on kijij, you can find some great deals on non current cameras. I shoot nikon so I'm going to tell you canon is worth its weight in keystone light but obviously thats false.

Lenses havent changed much, read professional reviews about new lenses... but if your coming from a GoPro it doesnt fucking matter if your lens has slightly less barrel distortion and worse CA then the version that is 2x the price. Check out Sigma 10-20mm (F/3.5) or Tokina 11-16mm if you want somethign hella wide. You will probably get a decent kit lens with your camera too tho.

Oh and heads up. Photography and Cinematography can be the most expensive hobbies. I have a BMW 3 series with a camera bag inside. The camera bag is worth more then the BMW. Be careful not to get sucked into spending a small fortune on lenses and gear and then slaving your life away in libraries and at work while your beloved camera gear sits in your closet.

T3i is nice and really worth the price. I would definitely go to a shop or something first though and ask a professional like the above poster said.

get the t3i, and don't forget the 50mm f1.8 lens. Cheapest setup, yet such quality

go on youtube and watch edits/videos with this camera, its really worth it and I am glad I got it

i have a t3i with the kit lens, and it's a great value for the money. definitely can't go wrong with it, as long as you don't need super high quality imagery.