Taxiing Cessna Cardinal pilot and Ground Controller failed to communicate the requirement to hold short of the active runway.

Narrative

Following maintenance on the aircraft; I was taxiing the aircraft back to its parking area on the other side of the runway. I contacted ground control on the radio; requested taxi to my parking area and was cleared to taxi; copying 'Taxi to parking; cross runway at Golf.' I read back the taxi clearance stating 'Taxi to parking; cross runway at Golf.' I began to taxi down the north taxiway toward Intersection G. Arriving there about 30 seconds later; I scanned up and down the runway prior to crossing. As I crossed onto the runway; Ground shouted 'Stop!' over the radio; and I stopped with my nose over the hold short markings; replying 'Stopping' afterwards. I observed an aircraft on short final; about 4;800 FT down the runway; begin a go-around. Following that; Ground gave me another clearance of 'Cross runway at Golf; taxi to parking' to which I replied 'Cross runway at Golf; taxi to parking;' and proceeded to do so. I completed the taxi and parked the aircraft in its tie-down place. Causation: The Ground Controller did not coordinate with the Tower Controller for the landing traffic when issuing me the clearance to cross the runway. If the clearance had been read back in error; then Ground did not clarify when I read back the clearance to cross the runway.