How would one go about picking parts to build a 1 moa rifle?

How would you know what works togeter and what doesn't?

If you gave me a White Oak or Compass Lake Engineering barrel, a free-float handguard, and a BCM upper receiver I could build the rest from 2x4 lumber and have a sub-MOA rifle.

I’m not joking.

Get a top-shelf non-chromed barrel (Criterion, WOA, CLE, or similar) with a Wylde chamber and a decent free-float rail, and quality ammo. To me, quality ammo means Sierra Match King, tipped Match King, or Berger bullets. I’m less concerned about who packaged them (handloads, IMI, Black Hills, etc.)

The rest of the build has very little impact on the mechanical accuracy of the rifle although trigger and optic will have an impact on the shooter’s ability to extract that mechanical accuracy. Trigger needs to be crisp but doesn’t need to be light. Optic needs a fine enough reticle to allow you to hold a sub-moa point of aim. It’s hard to hold sub-moa when your reticle has a 2moa center.

So, barrel, free-float rail, trigger, optic. The rest matters very little. The rest could be a $399 PSA kit and it would still shoot sub-moa.

My BA DMR 20" barrel shoots sub-MOA.  Aero upper, Aimsports handguard, Toolcraft BCG, Larue 2-stage trigger.  No MD, just a thread protector.  Athlon Midas BTR 2.5-15x scope in Aero mount.  It all boils down to the barrel, you can cheap out on the rest.  Well, you do need a decent optic as well.

Oh, and yes, handloads.

Don't go with cheap bottom dollar stuff, don't pussyfoot or hamhand assembly, and more likely than not it will do 0.4 MOA or less. ETA: I speak of mean radius, which should be standard.

If you use reasonable parts , any well built AR should do 1 inch .

I have a home assembled:
BA 18" stainless Wylde chambered heavy barrel (Free Floated)
$300 Burris 4-14x scope in Aero light mount (Scope was a clearance and display model at Academy few years back)
"G" G2S trigger
Shooting Hornady or PPU (Cheap) 75gr off the shelf ammo
All other parts are basic AR stuff

Even with the cheap PPU ammo easily shoots sub MOA without hardly trying. 300-400 yrd shots are boring unless windy and I am not a gifted shooter.
I "built" it to be a budget 500-600 yard gun to dip my toes in the 500 yard + shooting.
Only thing I plan to upgrade is the scope and mount.

I think a BA, Faxon or a Green Mountain barrel would get you there with a decent trigger and manufactured high end ammo.  

But....... I would personally go with a WOA barrel if I were after consistent grouping.

Barrel & trigger are the places you'll see the most results by spending a little more.  Then good sights/optic and mounts.  Get a great optic & put it on a shitty mount isn't going to do you any good.