We are too designing our own CNC Machine. We are also looking at using a ballscrew type design like you have above. There are many different configurations you can get. Take a look at Misumi as they you can get the ends configured how you would like. It looks like the 20mm portion of the shaft would be used for the nut that moves your axis. The 12mm on the right side is used for the bearing supports on the end of the shaft. The 15mm on the right is for the Fixed bearing block and the 12mm on the right would be to couple your ball screw to the motor shaft. Misumi has many configurable options for zero backlash shaft couplers. I didn't take a look to see, but I'm sure you can get a 12mm to 1/2" shaft coupler.
Hope this helps.