Finding out the maximum available supply then add say 20 percent is a good start.
You could work it out from the schematic but I would sugest it needs to be in the order of 300 Volt DC at least and a 'high quality' (low leakage) type, not ceramic.
Yes either would work fine.I think I would go for the polystyrene but if you have the patience you could try out both and see if you can notice any difference between the 2 types. Voltage rating is fine.
Make sure your soldering work is REALLY clean as the impedances around there are vety high and any flux or maybe even sweaty fingerprints may have some impact.
The B+ voltage looks to be 185v DC. The voltage divider, 560k and 270k will drop it to 60v DC. Measure the voltage at the junction of R36 and R37, it should be around 60v DC.
You can use any capacitor over 160v dc. I like Polystyrene in this spot. You may try several values from 470pf to 1500pf to see what you like best. Silver Mica is brighter.
The configuration of C16 and C21 could be improved. C21 being an electrolytic will not have the best sound or response. Changing that capacitor to a Polypropylene film capacitor will give the mic a better sound. Try the mic with and without C16 to see what you like better.
I think changing this cap to a higher value would make it sound darker or less articulate if you will. On a side: Examining the attachment, I can't figure out the purpose for the 2nd half of the 12AX7: cathode, grid and plate all hit ground. What's with that??