Rainier Arms deals Stag. I haven't used Stag or Rainier's barrels and I'm not sure who makes the barrels for them. That might be more important. I've seen the barrels and they look okay, but hey, it is a barrel. If they are contracted out through a good maker, I'd say go for it. Reason I bring up Rainier, is that you can't make a bad choice if you just want a shooter. Everything they sell is good for that.
The barrel is easily the single most important part of an AR. It determines the accuracy, weight, purpose (is it a short handy M4 or long heavy varmint rifle) and then some. If you just want a shooter, just for fun, the Stag barrels and the White Oak they carry (I've heard good stuff about White Oak by the way) should be fine. If you want a tough military grade rifle, look at the LMT or Noveske barrels. Noveske makes one out of SAW blanks, that is tough. If you want accuracy, the stainless ones usually work out better, but they don't last as long as the chromed bores. The groups open up faster, but start out tighter than chrome bores. Trade offs. Cut rifling is better but more expensive, if you want a tack driver, get cut rifling. A decent stainless barrel of whatever length you want should yield a good shooter. Your rifling rate is very important too. Get a 1/9, and forget about using the 77SMK's. 1/8 is the most common, but I prefer 1/7. I shoot 62gr. and higher usually. It will do 55's, but not as well as the 1/8 or 1/9. If you plan on using cheap ammo, surplus stuff, it usually is 55gr., so go with the 1/8 or 1/9, if you load or want the heavier, higher BC rounds, get the 1/7. Varmint shooters like 1/9 and sometimes even slower, 1/10 and up, but they also use 40gr. bullets.
A .750" stainless barrel will give you good accuracy and not too much weight. If you want a varmint or longer barrel, I'd get it heavier under the handguards. If you flute it, well, you have more options (and more cost). The M4 profile does nothing except for looks unless you plan on mounting a masterkey or grenade launcher, but they are common enough to sometimes be cheaper now.
You can actually splurge on a barrel and build junk around it and get a very accurate rifle. Sub MOA. On the other hand, you can build a top notch rifle, best parts available, and use a junk barrel and it will shoot six inch groups if lucky (saying you are stellar). That is how important barrel selection is on an AR.
The rest of the stuff should just be well made, either mil spec or better, and focused on reliability. The trigger, to me, is important, but some aren't so picky. I consider it to be right behind the barrel in selecting parts actually, since I select a trigger that will go well with the barrel.
The absolute best barrel you could get would be to go to Satern's site and see if they have an AR barrel already in stock that suits your needs (I have one on special order, have for a couple of months already, and it could be a year or more until I have it). Expect $400, but expect sub-moa. My Grendel is superb.
If you just want the shooter, and White Oak or Stag make a good one for half that, say $200 or so, that might not be a bad deal. Rainier also has a discount table. It has parts where someone buys a rifle, but wants them to change out one part for another I think. Good deals by the door, they always change. You can ask if they have a good barrel in there, they are new and there are always a few in there. Last time I was in there, they had a Noveske for $200, and a heavy White Oak (for about the same I think).
