How far away will you be? That should determine the focal length you need, and then get something fast in that focal length. Perhaps take a serious look at a prime like the 135L or the 200 2.8L (both under your budget) if they're long enough, or the Sigma 70-200 2.8 if you need a zoom that again, is within your budget. IS is nice, but not essential for action sports (can't stop movement with slow shutter speeds!). The AF on these lenses all have USM/HSM so they're nice and fast for use with AI Servo.
Oh also, grey ice won't be a result of your lens (mostly), but rather a result of underexposure. Regardless of what you are shooting, your camera will meter for it to be 18% grey. Read up a bit on exposure - lighter subject will require you to expose a stop or two over what your camera thinks is right - so shoot AV or TV, and crank EC up a stop or two, or learn to shoot full manual. A fast lens like the ones I listed above will help with this, as they'll let in more light and allow you to get those exposures needed.
Set the aperture (close to wide open in indoor light, really) and shutter speed you want (Ideally 1/500 at least for action sports, though you could probably get away with less) and crank your ISO up to get the right exposure. Remember to shoot at a speed of at least 1/shutter speed x 1.6 (XTi crop factor) to get sharp handheld shots.