I'm about to publish a very large service to ArcGIS Server 10.4.1 to be used in an AGOL web map and application. Usually, my organization just leaves our data our local projected coordinate system, which is based on NAD 83, before publishing. We have run into issues, particularly with our basemap layers, where we have had to apply a transformation in ArcMap to transform our data into WGS 1984 before publishing to be consumed in an AGOL web map.
Ultimately, I know both methods work if you are just consuming your service as an operational layer (rather than as a basemap layer), but which method would be considered the "best practice"? Which method will make your services run most smoothly?