I would imagine it will be DC servos on it, they are easy enough to test to see if they are running. All you need to do is hook them up to a car battery, reversing the polarity will move them the other way.
I would say keep the servos if they are good, depends on the specs of them but at that vintage I would imagine they are 140-160V. If you got Geckos then you would be limited to 80V so speed would not be the max but may well be adequate. You may need to get different encoders but you wont know that until you know the codes. Have a look at the motors and find out their current (continuous and peak) and their rated voltage, also if you can find out what the drives actual voltage was as it may well have been less than the rated voltage.
If the Servos are knackered then Steppers will certainly run the mill, they as you say are easy to set up but also Servos arent that difficult to set up. If I had a choice I would go servos.
Power supply will just need to be a transformer, rectifier and capacitor whichever route you take (servo or stepper)
I have PMDX 122 breakouts and also CNC Building Block Acustep (although no longer made
 ) Both are excellent boards. I have never had the CNC4PC or Campbell ones so cant comment on them.
Yes keep the belt drive, will make things easier to connect up and if it was good for the original then its certainly good enough for it now
Rigid tapping is probably not possible at this point, using a floating holder will be but is dependant on your spindle motor/control.
Hood