If you can manage a trip to one of the stores, I would recommend it. You can use the bore tools and light to find a field or rack grade that has a decent barrel. You can also take your pick of different serial numbers.
My Dad and I did that. We were able to stop by the Shiloh battlefield on the way. I heard there was a Hank Williams muzeum in southern AL, but I didn't hear about that until later.
The CMP store also had some correct and collector's grade rifles out there. They weren't cheap though.
I picked up some Greek ammo as well. It was neat seeing all those crates of ammo stacked up out back when I went around to pick it up.
Also, the people working there were all real nice. The other customers were also but it seemed that most were local. Not a single comment despite wearing all maroon Texas A&M shirts the whole time while in AL.
CMP also sells new barrels and stocks if you want to buy a rack and upgrade it.