Let's build an AR15

Monopolize away! Some of us here have never had anything but bargain basement off-the-rack specials, and it's interesting to see what all goes into a quality piece.

In my opinion, a quality barrel and good bedding, hence my love of bcm uppers that have to be thermfitted. You freeze the barrels to shrink them and use a gentle heat source such as a hair dryer on the upper to make them go together. I'm not a snob for handguards, as long as they're free floating.
The only factory carbine I bought was a dpms lite 16 and it would shoot sub moa with my hand loads. I did my standard bench rest stuff to them, turning the necks to make them uniform, uniforming the flasholes, etc. So, I think your bargain basement likely will be fairly accurate with good ammo.
My quest top build an AR-15 that would show well in bench rest never got to that level. Obviously, I'm not in the same league as Speedy Gonzales or Tony Boyer, but I wouldn't be embarrassed at a match. When I used to shoot, quite a few club members would express their surprise at what I could do with an AR-15.
After a good barrel, the most important thing is attention to detail in putting it together, free floating the gas tube is a biggie.