INRE: CRS ( coordinate reference system ) depends on the size, shape ( and aspect ratio) and distribution of your collection, and whether 'orientation' is relative others within the collection, or relative to other external data. i.e. is it a string of pearls over several hundred miles or a more or less ellipsoidal blob a few kilometers across. If I am dealing with a more or less random set of objects like an island chain in first case, I create a user defined projection suitable for the data like a two point equidistant. More advice at http://www.geo.hunter.cuny.edu/~jochen/gtech201/lectures/lec6concepts/map%20coordinate%20systems/how%20to%20choose%20a%20projection.htm

As to auto-magically generating derived features and data, this is a common geomorphological problem, like evaluating glaciers or sandbars in a river, ponds, etc. And again, it heavily depends on the features and expectations - if your shapes are spirals or lave holes and islands, it gets way complex. You can get along way though with chaining the various standard tools like boundary geometry ( https://docs.qgis.org/3.34/en/docs/user_manual/processing_algs/qgis/vectorgeometry.html#minimum-bounding-geometry ) - see attached example derived from a Lidar dataset using QGIS standard tools to detect frequency distribution of angles.