I started out with a T3i. Shot as much as I could to get the technical stuff aside. Eventually sold it and purchased a 5D Mark ii. Learned more, practiced every day. Then I sold that and bought a Blackmagic Pocket Cinema Camera so that I could learn how to work with RAW files. I had a GH3, sold it. I shoot on REDs at work but own a GH4 (very similar to the GH3). Once you understand the basic concepts of how a camera works, you'll be able to pick up any camera and figure it out quickly. After owning and shooting on so many different cameras, I have realized that the camera is only a fraction of what matters. The most important thing is what you're pointing your camera at and how you choose to show the subject. At the end of the day we're trying to tell stories and if you can pull that off, no one will care which camera model you shot it with.
But since you do need a camera before you can film, I'd recommend staying away from Canon. I swore by them for a while but have grown away from them as they offer only what they have to in order to stay in the market. I'd honestly suggest a GH3. They're robust (I took mine to Afghanistan), they can shoot 1080p at 60fps, they offer convenient settings for film on a photographic oriented camera and panasonic is really trying to push the bar and offer more bang for the buck.
Good luck on your search!
Best of luck,