I'd say you need to consider exactly how you define "long range". Are you talking 1K meters? If so, that will limit your choices of bullets--and you might want to consider stepping up to a cartridge case with more internal volume than .223 Remington.
Also--how do you define "precision"? If you were able to hit a 10 inch plate consistently at (say) 600 yards, would that satisfy you? If so, the world is your oyster--any decent barrel should give you 1.5 MOA in accuracy. Now it's on you to learn to read the wind, and you can do it all day long.
If your definition of "accuracy" is to consistently shoot 30 rounds into 1 raggged hole 1/2 inch across at 100 yards, well that is another (more expensive) standard you have set for yourself.
The most accurate bullets at long range tend to be heavier, longer, and more streamlined. Heavier, longer, more streamlined bullets will do best with a 1/7 barrel twist. Heavier, longer, more streamlined bullets ALSO tend to be more expensive. Do you reload? If not, are you willing to either pay .75 to $1 a round OR put up with shooting mediocre groups?
If (on reflection) you want to divide your shooting between heavy, precise, expensive bullets at 600 yards, and cheaper 55 grain plinking bullets at closer ranges (50-250 yards), consider going with a 1/8 twist barrel.
As for barrel weight, if you plan on always shooting from a bench, go with a bull barrel.
If you plan on carrying your rifle quite a bit, the extra weight gets old fast.
If you are new to long-range shooting, go watch the Sniper 101 series on Youtube.
SNIPER 101 - YouTube
He'll get you up to speed pretty quick with relevant information, including cartridge selection. You just have fast-forward to the relevant content through the head-banger music intros.
Inre: barrels--yeah the Krieger, Bartlein, Douglas barrels are all quite good, and they are a bit spendy--but I think the Larue barrels are a very good value at the price point (do spend the extra $20 for the M4 feed ramps).
5.56 Stealth Barrel - LaRue Tactical
Out of the box, the Rock Rivers uppers I've seen have a real good reputation for 3/4 MOA accuracy.
I think I read that they use Wilson stainless blanks:
Wilson Arms 20" .223 Wylde 1x8 Stainless Steel Bull Barrel Stripped
If you're building from scratch, consider going with a stiffer upper receiver than the M4 flat-top (read: billet upper receiver), if you want to hang a lot of weight off the front end.
I think this (MEGA Part# MKM620HA $279) is a smoking deal on a billet upper and free-floated forearm--if you can take heckling from the gear-queers over the uncool Keymod holes:
https://www.brownells.com/rifle-parts/receiver-parts/receivers/upper-receivers/ar-15-5-56mm-assembled-upper-receivers-keymod-prod113025.aspx?avs|Special-Filters_1=Salezz1zzClearance&avs|Manufacturer_1=MEGA+ARMS
The MKM620HA is a 16" Free-floated forend.
Google the part number for pics.
Good luck with your build.