I did a course on cartography a couple of years ago, and one of the better assignments was to find a suitable projection and make a proper map describing a comparison in distances between two points. The projection I used was of course Two-Point Equidistant Projection (the only possible one).

My resulting map is on the last page here: https://adelie.antarkt.is/aron/l0020b.pdf

EDIT: Apparently it was one of my GIS courses, not the cartographic one, which were more color theory and labels.

One bad thing about the projection is that great circles are curved, so my straight lines should have been curved as well.