You say you want the best raw footage, but I doubt you actually want to shoot with RAW do you?
With the budget you've got, RAW isn't the path, unless you do have a scorching fast computer with tons of HDD space, and the extra budget for cards or even off-camera recorders + extra SDDs.
Now, the new Blackmagic Pocket Cinema camera looks very promising, as it can shoot RAW, but also ProRes in near full quality with a lot of the dynamic range and color data preserved. Shooting in prores will save you space, editing time and for most situations just as useful as RAW, but all without the hassle of working with it.
The BMPC is only a $1000 camera and there's all sorts of lenses out there, and I'm basing a lot of this on what Andrew has said on EOSHD, but the new Sigma 18-35mm + speed booster for mFT is just about the best set there is, and all of that together with some fast cards and batteries is just about your budget.
The camera itself is small, very easy to rig up, and it has pretty good low light performance, although a draw back could be it's small sensor, the lens choice I just suggested should cover most everything, just need to grab a decent telephoto for sports work.
Personally I've got a Panny GH3, Olympus 12mm F2 and Panny 25mm F1.4 for video stuff, with extra battery and new 64GB card it was all just about 2000 USD. The quality of image, 1080P up to 60FPS, usability of manual controls, tilt screen for tight angles, overall small size and low weight along with the high bit rate and nicely editable MOV files makes it a versatile video camera. I did choose this mostly because I needed a second stills camera as well, so it fit the bill, and have been impressed with how well it does.
Really, I would like to try out the Pocket Cinema camera, but if i can afford it I would get a 5DIII and install the ML hack for RAW video on that for the absolute in image quality and low light performance... but again, with all the high speed cards I can't get close to that set up