All I can speak for is my own experience, witch is limited. I only have two rifles that do not have factory barrels. One is a .400 Whelen, Winchester 70 action with a Shilen barrel, it shoots very well and cleans easy too. This rifle had been built for the person I bought it from, he had not shot it.
The other rifle is a Savage 111 action that I installed a E.R. Shaw 35 Whelen barrel on, it is a prefit barrel kit. I got it on sale for $163. At the time I was looking for a 35 Whelen bolt rifle but did not have a lot of money at the time. I also wanted a faster twist than the 1-16 that Remington's and most Ruger's have. The E. R. Shaw has a 1-14 twist, 24" and listed as a medium magnum contour, with scope the rifle weighs about 8.5 pounds, I don't mind the weight. As for accuracy it puts my hand loads with Speer 220gr and Nosler 225gr. bullets at 1/4" or less at 100 yards as long as I do my part. I love it and I was able to do it all my self.
My conclusion is if I was to do another rifle and wanting or needing to stay on a small budget I'd use a Savage action and an E. R. Shaw barrel prefit kit. If I was going to have a gunsmith build me a rifle I would use a different barrel, probably a Shilen. The reason for this is there are different grades of quality of every thing and if I'm going to pay a gunsmith to fit a barrel for me I may as well go for a higher quality barrel. When you look at the price by the time you the barrel and pay some one to fit it for you it's not really that much different. If you need to stay on a very tight budget and can do it your self I don't think you can go wrong with a Savage action and an E. R. Shaw barrel kit. It's going to come down to can and are you willing or wonting to do it your self, what you really wont, how much you want to or can spend, or how long you are willing to save for what you want. For a rifle build take your time look at the options and make shore your going to like what you go with, ether way it's a fair amount of money to be forking out, so make shore it is what your going to like.