"0" reference point on CNC lathe

I am just getting into programming and running CNC lathes. Where do
most of you set your "0" reference point for your tool offsets on the
lathe? At the chuck face or somewhere beyond the end of the work?
Do you change this point for different parts? My software has a home
position whick is at the far right and tool back toward the front
which is also where the axis readouts are "0.0". The tool reference
point can be set anywhere from this point.

Thanks

Scott Hamilton