Are you going to be using a nutted prefit?
If not, whoever is fitting your barrel should do the work. You want one "source" for the build to avoid any finger-pointing after if there are any issues.
JMO...when it comes to must hunting rifles (specifically excluding long-range hunting), going full Monty on truing has diminishing returns.
Shooting game at "typical" ranges limited to a few hundred yards doesn't require any more than minute of angle accuracy which is easily achievable with no action work at all. A quality barrel/chambering job will get you there and then some.
I would routinely face the receiver, and then check for amount of contact with lugs/abutments and see if they needed work beyond lapping.
If cost is no object, go for it. But for someone on a budget, I'd tell them to put the money into glass/trigger/stock instead of single-pointing threads, reaming the raceway, or other higher-end items that are part of a "full" truing job.
There is no set definition of what "truing" consists of- so when you get quoted a price for it- drill down and get the specifics of exactly what's included.
