You only have one source or 240/120 in your building, an additional 120v line originates from the same source, so it does not really matter as long as you run everything in the correct size conductors, and fuse accordingly.
You should run a system ground to the machine and bond everything to this common ground point, the ground should also be run to the VFD and then on to the motor frame, with the 3 ph conductors for the motor twisted together, and preferably run in metallic or metallic liquid seal conduit.
There are many previous posts on this subject.
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.