How to decide print orientation?
To answer the generic question "Is there a thought process for how to orient the part for printing?", I would say "Yes there absolutely is such a process!".

Part of this though process can be aesthetics, structural strength, limiting filament waste, print duration, etc.

For the given example I would try to think of the load case (if it has to bear a load) that subjects the part and prevent a perpendicular load to the deposition plane. If the load is low or non existent, you could orientate the print such that you minimize wasting material, or get the best aesthetics (removing supports can leave its scars).