The colour temperature of the lamps on stages is around 3200 to 3400 degrees Kelvin. If you set your camera to those settings, you will be fine. However you said you have a $300 digital camera, this means it is a point and shoot so does not have all the controls a DSLR has.
In your case,set the white balance to incandescent and go from there. Get a meter reading on the stage and then set the camera to match those exposure settings and off "auto". I would hope that a $300 P&S camera would have shutter or aperture priority metering modes
Blur is caused by camera or subject movement.
Set the cameras ISO to its highest setting and shoot with the lens wide open. If there is too much noise, you can later process the image through a program like Noise Ninja to clean it up, but you will have little or no blur