Not really in the spirit of doing it from the basics but the plugin "Bool Tools" from Smustard really helps with deletion of unwanted geometry. It costs $10 but you soon save the time to make it worthwhile.

Hi folks. Don't forget that you can use "Explode curve" to transform a circle or polygon or freehand curve into a serie of edges. After that, you can delete selected edges withoout erasing the whole lot. Just ideas.