Interference is a combination of many factors too numerous to attempt to cover in this post.
First, the computer operation can cause interference thru the 120 VAC voltage source. Also a small amount of RF energy could be radiated inside the enclosure by the computer. My recommendation is that the computer itself be outside the CNC electronics enclosure.
As far as other interference, it can come inside the electronics enclosure thru the 120 VAC power. I personally recommend an EMI/RFI filter on the incoming power source. I built my enclosure with one.
If at all possible, do NOT use a switching (switch mode) power supply. The method of operation of switching supplies creates EMI in the power source, and can also radiate some amount of RFI depending upon the switching frequency.
Keep all wiring as short as possible.
Make sure that your power supply output leads have 6 twists per foot.
Use a VERY large filter capacitor rated at approximately 2 times the power supply voltage.
use shielded wiring where possible.
Keep the power supply as far away as possible from the drive enclosures.
Have only a SINGLE ground point for the power system. Different ground points can cause ground loops which are almost impossible to troubleshoot.
Hope the above gets you started.