To the OP:
You asked the question, "what goes into a custom rifle?" I'll try to answer that for you.
1. A lot of custom riflesmiths use the Remington action, because it is arguably the most common and available action out there--and it's an excellent basis for a custom rifle. But, buying the action is only the first step.
The custom builder then does the following:
a. Blueprint the action. This means machining and fitting parts so that they are exactly to the original specification.
b. True the action. Tolerances are tightened considerably; locking lugs have 100% concentric contact with the locking surfaces. The bolt face is squared; the ejector and extractor is adjusted and tuned for 100% engagement and reliability.
c. The lockwork (trigger assembly) is tuned and adjusted for a clean, crisp repeatable pull weight that is safe to work with.
d. The recoil lug is usually replaced with a precision ground lug that will be perfectly square to the receiver face, and also perfectly square to the barrel shoulder.
e. A precision barrel is selected. Usually this means a Kreiger, Bartlein or Obermayer barrel--these three are rifled using the single-point cut method. The rifling is cut one groove at a time, with the cutter removing a minute amount of metal each time. After the rifling, the barrel is gauged to a most exacting standard. Cut rifled barrels hold the standard for extreme accuracy.
f. The chamber is cut to tight specifications to hold the ogive of the chambered round very close to the lands, perfectly centered in the bore of the rifle. The crown is finished, usually with a counterbore to protect the crown itself. The bore is then hand lapped to a mirror finish.
g. The stock is then mated to the action carefully; bedded and mounted with extreme care and precision.
Be well advised that quality doesn't come cheap. The wait times can be as long as a year or more. But if you have patience, and can pay the tariff, you will get a rifle that is a dream to shoot.
And since you mentioned Texas Brigade Armory:
This is the M40A3, with a few options.
Built on the Remington 700 action, with a 20 MOA base, and Badger Ordnance DBM. It uses AICS magazines, in .308 Winchester.
The optic is the 8-32x56 Nightforce NXS, with mil-dot reticle.
It also has a Harris swivel bipod, and it's in the McMillan A3 stock. The barrel is a 26 inch Bartlein, 1-11.25 twist.
If you want to carry it, be prepared--the rifle weighs 16 lb, with scope. Yes, it's a heavy beast. But Mike Lau--who does ALL the building on his rifles--guarantees 1/4 minute groups with match ammo in all conditions. This rifle does BETTER--it's the most accurate rifle I own, and outshoots a .220 Swift benchrest rifle that I have.
It's not cheap--with the scope and tripod, I have over $5500.00 invested. But, for the rifle's purpose and end use (it is a duty rifle) it is money well spent.
I hope that this helps you in your decision.