10.5 x 25 cnc plasma table retrofit

Do you also have the drives ?

Find info on the drives, check wiring and if it is in good condition try to power everything up, check drives for errors or strange behavior or smoke, then we can move to testing drives and figuring out what controller you would need.

First picture, the black servo positioning something or another is what we today call THC, and all that (but much faster) today fits in half a cigarette box! I would get rid of this so fast....
The attached picture with 4 boards, the left one is the power supply for the next 3, those 3 are the servo drives with lots of electronics, so i would really try to save this, do not worry about the broken encoder connectors, encoders should now be wired to Mesa board.
The box with PLC, i would also get rid of this, fast, all that is now done in software and through a Mesa board.
I would suggest getting a Mesa 7i96S with 7i85 and 7i83 and THCAD for now as this will be good for analog (existing drives) and new drives with analog or step/dir controls.
There are cheaper combos or single board solutions like Mesa 7i97T that everything for analog servos and encoder feedback, or 7i92TM with 7i77 that is the same things functionally.
For new dives with no feedback to LinuxCNC, 7i96S should be enough and you can add 7i85 for encoder feedback at any time later, or single board solution with encoder feedback = Mesa 7i95

Z axis is in the rapid servo positioner box, aka the old THC, so that would need replacing, a cheap stepper drive and motor should do just fine.