I have a shapefile of different administrative regions that are in all 50 states in the USA. I also have many lat/long coordinates, and I'm using NNJoin in QGIS to find the distance from each point to the nearest polygon.

I'm wondering which projection (if any) should I use to minimize distortion when calculating distances in the entire USA region? Or would it be better to do three batches, one for contiguous USA, one for Alaska and one for Hawaii (if so, which projections then)?