About vertices/faces reduction and optimization

I have been pondering if the mesh of a scanned model I have be made with a better mesh and if that would help with a better smoothing including along the interface between the flat sides and the curved side. Original STL, Screenshot

JA12 introduced me to the idea of turning the triangles to quads. I had no idea such a thing existed. Previously, I understood that triangles were how it is. gradyp suggested that I could get another mesh that represents the shape just as well, but is better. I was expecting something like this and this. Sorry for my poor paint skills in the mockups. Instead got this and this. After some fiddling/reading around, I used the Remesh modifier to get this. Admittedly, it looks better than the mockup I made in paint, I got fewer vertices and faces, and it does calculate the smoothing a lot faster.

Is there something better? It would be great if I could get some explanation of, or pointers thereto, about optimizing meshes. I have no idea if the above made any sense. As I recount my story, I feel like I am missing a lot of pieces of the story, just saying things while not being at all sure about what is happening under the hood or the fundamental principles.