Sensor - for a range of like a foot of distance, won't accidentally trip, good in case of different textures of the papers
Finding good parts for a good price (sensor, input keypad, led signs...)
Externally power led signs? How to hook up two signs?
What model of Arduino is appropriate?
Light Beam, when broken increment count. (if there is a distance between the stacks)Here
LED signs or counters?Herehttp://www.gammon.com.au/forum/?id=11516
Search EBAY example Here
UNO or Mega depends on how you drive the counter.