I'd suggest 'Fullmetal Alchemist'. It shares similarities with 'Origin' in terms of the depth of the world-building and the emotional impact of the story. The way the plot unfolds and the character interactions are comparable too.
Adam's comic drawing skills grow through continuous learning and experimentation. He studies different styles and techniques, and incorporates what works for him into his own art.
I think it could represent a person's extreme response or a satirical take on a common situation. The finger down the throat and vomiting might be a metaphor for getting rid of something unwanted or expressing deep dissatisfaction. The New Yorker style often brings a unique and sometimes cryptic perspective to such imagery.
A good cartoon basement for kids to draw would have plenty of space, good lighting, and maybe some examples or templates to get them started. Also, having a variety of drawing tools available would be helpful.