You've never done this before and want to do it the hard way.
The great thing about Savage rifles is that barrel swaps are easy because of the barrel nut.
You have more dimensions to worry about when installing a Remington style barrel flush against the action shoulder. You want minimum clearance between the barrel and the bolt, this requires accurately measuring the front of the rifle action's depth to the forward edge of the bolt. Your tenon and barrel shoulder needs to be precisely cut to the proper length so:
1. Your barrel never binds against the bolt when it's closed.
2. You don't have any more than a minimum gap so the case is fully supported when fired. Tighter and looser standards are held by various gunsmiths. Do some research for your intended caliber.
Once the barrel shoulder is set so the barrel tenon length is perfect, then you can remove the barrel and carefully hand turn the chamber reamer a little at a time until you get close to being able to close the bolt on a SAAMI Go-Gage. This means re-installing the barrel to check your work or trying to stay centered in the bore while the barrel is installed and working through the rear of the receiver. Do not remove any more material than it takes to just close on the gage. The barrel needs to be torqued to the receiver to get accurate measurements.
Savage barrels and receivers using the nut is easy as hell. Simply remove the extractor and ejector from the bolt, screw the barrel in and install a SAAMI Go-Gage in the chamber. Screw the barrel down snug on the SAAMI G0-Gage and torque the barrel nut in place. Double check to insure the barrel won't close on a No-Go gage, still closes on the Go-Gage and you're done.