The GM tube draws nothing, unless an event happens. The current peak (maybe 100us long) is usually limited with a resistor like 5-10Meg.
Normally you get a ~dozen ticks per minute, unless you mess with some active material.. (PS: don't do it at home(!!), but an old WWII meter's dial from a Junkers plane makes 4000 ticks per minute even today

). Mind the GM tubes have a limited life, based on number of events.
The power supply I built in past consisted of 3 transistors, a choke, 3 fast diodes with 3 10n/600V caps and 3 150V zeners as the feedback to get something stable like 450V. I will search for the schematics, the GM stuff worked several months off a 9V battery..
PS: MPSA42 was the driver afaik..
Ok, here - the second schematics from top was the one, we built several and it worked fine:
http://www.techlib.com/science/geiger.htmlThe HV diodes were some "fast" 1000V diodes as I can remember, not sure the 1n4007 is the best choice there..