Neutral goes to the lamp socket shell that is more likely to be touched accidentally. Hot goes to the center contact inside the socket.
Usually the screws are "sort of" color coded with silver plating for neutral.
For an all plastic bodied fixture, leave the ground wire coming into the box curled up and unconnected, or connect it to the box itself if the box is metal.
When cleaning anything including baby diapers, it is better to sweep off or scrape off as much solid and semisolid material as you can first. (1) Less cleaning fluid or detergent needs to be used, (2) Less of a mushy mess which in turn means that bleaches or disinfectants will be more effective.