Medical, first responders, food/groceries, trade work? Thats kinda where my list starts, obviously pretty broad, but its a place to start. Trade work could be minimized as well. Just need them for emergencies.
Yes, but the problem is it snowballs. I work at a plant that makes processed food, essential right. Now if we have a shortage on packaging materials (boxes or plastic film) or shortage on parts for our equipment, or even gloves, hair nets and beard nets, we can't run effectively.
So now you just made all the suppliers of these things essential to keep the primary essential industry going. It gets to be a complex spider web of what is needed.