Ralph's description/diagram above is beautiful. Shows all of the components required to make a professional CNC system and how they interact with each other.
So the plan at this point:
Closed loop system, loop closed at the controller, no real point in discussing the other options.
The brain of the system is the motion controller. This could be Galil, Dynomotion, Centroid, or Mesa.
PC running the CNC software and providing the user interface. In this case would be connected to the controller via Ethernet or USB cable.
One drive required for each axis motor (3), compatible drives currently exist in the machine. Ignore the fact that Galil does have optional built in servo drives available.
Position feedback devices (encoders) can be linear or rotary. Recommend linear magnetic. One for each powered axis (X, Y, Z (quill)), plus the knee. (4)
Appropriate power supplies to run everything.
If you are going to go with a Galil, a DMC-4040 4 axis unit from eBay would be my choice. The last DMC-4040 I bought was $112, retail price is $2295 for the base unit from Galil. A fully loaded DMC-4040 with 4 built in 160V, 750W drives is $3530. Stay away from the 41x3 units.
Just a bit of clarification, a BOB is just simply a
Break
Out
Board, something to connect wires to (normally with screw terminals), since it would be difficult to solder wires directly to the controller chip. The controller manufactures bring out the connections on the controller board to some type of plug connectors or screw terminals. Galil for instance uses D-sub connectors on their units, there are many options available to break those out to screw terminals.
An example:
https://www.amazon.com/D-SUB-Terminal-Breakout-Connector-Screws/dp/B0779WGQN4