KE7GKP:
You must have a very different definition of "cheap" if you are looking for that resolution and speed. Good luck.
I believe the RepRap project gets those kinds of distance and resolution, but nowhere near that kind of speed.
If you want that kind of speed AND resolution, you are probably looking at something more capable (and more ($$$) than Arduino.
I'm not sure the Arduino would be the limiting factor; I think the limiting factor will likely be the hardware. To keep that level of resolution, repeatability and speed, you're going to likely need to use brushless DC motors (for the speed and torque), 16 bit binary encoders, and multi-start ACME thread screws (with anti-backlash traveling nuts) for each axis. None of that is going to be anywhere near cheap (heh - just price out the ACME thread screws if you don't believe me).
I actually think the Arduino could handle everything else (well, if you dedicated one Arduino per axis)...