Higher voltages will make the capacitors charge up to a higher voltage and higher current sources will make it charge faster.
Microwave transformers connected are very dangerous don't use them unless you know what you're doing as the output voltage and current is more than enough to kill, in fact it's a lot more dangerous than the mains.
Using a microwave transformer in this project is a bit safer, but still dangerous as a 12V pulse can still create a back emf of hundereds of volts on the primary which can be steped up to >5kV.
If you really want to use a microwave transformer in this project connect the mains side to the output transistor but don't blame me if anything bad happens.
A DC mains adaptor transformer is perfect for this, cut it open and remove the transformer, connect the low voltage side to the output transistor and the mains side to the diode and capacitors, if the voltage is too low then try swapping the connections on either the low voltage or high voltage side.
Be warned though big capacitors charged to high voltages can kill you and be carefull the voltage doesn't exceed the maximum rating of the capacitors or the will explode.