Suppose you have a string of resistors with one end of the string connected to ground and the other end of the string connected to 60 KV RMS, 60 hertz.
There will be stray capacitance from each resistor to ground. If the impedance of the stray capacitance is less than the resistance of the resistor, there will be unequal voltage across each resistor. The resistor connected to the 60 KV will have much higher voltage across it than the resistor connected to ground.
To correct the voltage unbalance, a capacitor with much larger capacitance than the stray capacitance is connected across each resistor.
To really understand what is being described, you should draw the circuit and do some calculations.
The same thing also happens with a rectifier string, except that the calculations are considerably more difficult.
Avalanche diodes as suggested by Gunnar are sometimes used (instead of resistors and capacitors)for low current high voltage rectifiers and the use of transient voltage suppressors (instead of resistors and capacitors) is probably a more modern approach.
You may discover that is is lower cost to purchase a complete rectifier assembly rather than design and build it yourself.
Good Luck, it sounds like a fun job.
Carl Pugh