It depends. Do you have a Remington take-off barrel or a new barrel blank that needs all the machining done?
Most gunsmiths post their prices on their websites. The best ones are not cheap, the bad ones (usually local yocals) shouldn't be used.
If just want a hunting rifle and don't want any of the usual accuracy upgrades (truing the receiver and bolt face and lapping the lugs) and have all the parts and they fit it won't break the bank. If they have to do all the machining to the barrel blank - profile, crown, thread, chamber and headspace you're looking at $400 or more.
I have hired simple projects out to local gunsmiths and they have on occasion butchered my firearms. I use "nationally known" nowadays and am happy to pay the premium. Wait times are always longer than I like, but the finished product is perfect.
Gre-Tan Rifles
Ken Warner
Alex Sitman
Dwight Scott
Depending what you need done, these guys rock. A lot of other top names are sure to do a great job. www.accurateshooter.com has a list of their gunsmith "top picks", you can't go wrong with any of them.