Over the years, I have had a lot of barrels put on actions, both custom and std factory, trued and non-trued Rem 700, 40x, Savages, A bolts, and Howa's.
I learned a very important lesson relating to accuracy that is rarely if ever spoken of. The gunsmith that indicates the barrel into the .0001 is going to produce an incredibly accurate barrel. The gunsmith you choose should bore scope the barrel before chambering, and the very best gunsmiths should gauge the barrel in inside dia uniformity from end to end as loose and tight spots in the barrel make for some bad harmonics. The aforementioned is where the rubber meets the road. You can throw money at a barrel, action, or scope, but if the job of chambering is not done correctly and thoroughly, 1/2"-5/8" accuracy may be the best you can hope for with a lot of work.
I am not a gunsmith, but have had some world-class gunsmiths as best friends over the years.
Building a rifle is different for many, I want the extremes in accuracy first and foremost, but many want the looks and what is most popular at the time, it is a hobby, make it fun for you.
At one time, all I would own was custom actions. A best friend and hunting partner passed away in a gunshop picking up his Shilen Barrel'd Parker Hale in 6 Rem. I had given him the barrel as a Christmas present. He had a Ruger 77 Tang safety with a Shilen barrel on it in 6 Rem also. Those two guns sat around for years in my gun safe, and I finally put a Leupold 36x on the Parker Hale with it's new Shilen barrel with a zero freebore chamber. First trip to the range with 62g Watson bullets/Win 760 at 4000 fps, I was shooting groups in the 2's. My benchrest shooting buddies could not believe the Mauser shooting to that degree of accuracy, even after showing them the targets.
Next, I pulled out the Ruger with its Newish Shilen 6 Rem barrel on it with its zero freebore chambers. The 80g Sierra at 3500 fps was shooting groups in the high 2's with little effort, over the max book charge of IMR 4064.
This was a very humbling experience for me to see these Junker rifles shoot so well. To further test my flawed thinking that it took a custom action to shoot extremely well, I bought a Savage and put a Hart barrel on it, it too shot tiny groups.
Well, the old saying, "First Comes Pride, then the Fall" certainly applied to me at that moment as the Piece of crap Savage which seemed like a contraption of an action, which just shot tiny group after tiny group.
So, the pride of ownership is a huge factor in building a rifle, perhaps the envy of some.
The Men that chambered these rifles were master machinists, and we spoke of bore dia, bore uniformity, with a slight choke of .0001-.0002 highly cherished when we could get a barrel like that, if there was a sweep in the barrel where the bullet entered the bore, how straight or off center the bore was in the barrel, and if there was a sweep in the bore where the bullet exited the barrel. Don't expect these master machinists to work for cheap, but it is the best money you could spend. It is also humbling to find some of the custom barrels that are very rough in the bore, and it is a real ****er to find that the level of roughness is now acceptable due to how high the demand is, and then find that customer service after the sale is horrible. That gunsmith by finding the problem(s) has just saved you hundreds of dollars.
So, hunt for those great machinists, and be grateful for them when you find them, then pick any action you like. My favorite custom actions are made by Jim Borden. Mr. Borden has incredible integrity and his integrity has been well established over the years.