The issue of upgrades is predicated, IMO, by first assuring that you have a decent candidate. The barrels, especially, must be sound and in good condition. When I have a gun redone, I always start with the fundamental - barrels, then internals made as perfect as possible, and any worn parts repaired or replaced.
The next critical issue is stock condition and gun fit. I shoot left handed and ofen choose to restock a resotration/upgrade. Not always, though. At this time, better wood is an obvious thing to do, since a new stock from a quality stocker is going to cost a fair amount of change - three to five times what you pay for the wood.
Gun engraving is up to the owner's whim, but I often choose to pick up the original engraving to preserve the 'originality' of the gun. Metal finishing in all cases should be consistent with what is proper for the gun in question. This usually means charcoal and nitre blacking/blueing of furniture , pins, etc. Cold rust bluing of the barrels if needed, and possibly re-case hardening the action if it was polished or annealed during the work.
The gun then needs to be assembled and final adjustments made by the smith.