I would say the power grid and the equipment which makes it work should be a higher, if not the highest, priority. Without electricity, it's "game over" across the board.
Another high priority would be energy supplies, especially delivery of gas/diesel. I recall a number of years ago when the Phoenix metro area lost about 70% of its gasoline supplies due to a pipeline rupture which took about two weeks to repair. They trucked in as much gas as they could, but it still was quite a mess, with long lines at the gas pumps and violence breaking out in some instances.
Previous blackouts in the northeast led to utter chaos within just a few hours.
I don't know if guns would have been necessary. If guns weren't available, then someone with the knowhow could rig up some sort of explosive device - or just set a fire.