How to determine Current draw from datasheet (shift register)

I am working with the 74HC595 shift register, its outputs connected to several LEDs. Datasheet here: http://www.nxp.com/documents/data_sheet/74HC_HCT595.pdf

I would like to know how much current this shift register will draw for its own operation (i.e., EXCLUDING the current drawn by LEDs/whatever is connected to it). In other words, if I have all connected Leds switched OFF, what will be the current drawn by the 74HC595 alone?

Which parameter should I look for in the datasheet? (It lists multiple Current parameters, and I am a little confused)

I'd go with this #:

"Low Power Consumption: 80-?A (Max) ICC"
Icc from the bottom of page 6.

"All unused inputs of the device must be held at VCC or GND to ensure proper device operation. See the TI application report,
Implications of Slow or Floating CMOS Inputs, literature number SCBA004."

For simple CMOS logic chips like this you can approximate the current consumption as zero unless you clock at high speeds (MHz...) Although this chip's spec is 80uA, that's worst case at high temperature, if you measure it at room temperature then expect a few nA upto a few uA in the static state.

You'll find for a more complex CMOS device like the ATmega328 the current consumption is basically linearly dependent on the system clock frequency as each gate that changes state on those clock edges will leak a pulse of charge as the FETs switch.