What's your definition of "cheap"?
With lots of light on your subject, most cameras (even many consumer DV cameras) will allow you to set the shutter speed to be fast enough to minimize motion blur. I think even the little canon ZR series cameras I used for some MMP mocap would go as high as 1/1000 of a second.
Frame rate and resolution on consumer DV cameras is very limited, though. NTSC cameras generally shoot 60 fields per second, PAL at 50 fields per second. If the motion is dramatic enough (not subtle movements) this resolution and speed can be useful.
Some HDV cameras can shoot at 60fps at higher resolutions than DV, but they may not be what you consider cheap. (or maybe they are)
Other than that, your start getting into specialized cameras, which generally involve .... specialized pricing. 
Haven't heard of the optitrak, but 1 bit sounds, well, a bit limiting.
The "softeness" of a marker shape as seen by an 8 bit camera actually helps the 2D tracker's accuracy at a sub-pixel level. 8 bit grayscale should be fine, but 1 bit would likely make 2D accuracy a challenge.
