I am not sure about getting a square wave from a GM tube it is more like a pulse.
I would recommend that you get one edge of this signal to trigger an interrupt and let the ISR do the counting. Then use the millis() timer to see how many counts you get in a second to give you the rate.
http://www.arduino.cc/playground/Code/Interrupts
Are you going to incorporate dead time correction or do you want just the raw rate you read?