The lower: Buy a lower. Any Lower. They are mill spec.
Nope. Stay away from any polymer lower. Forged lowers: stick with 7075-T6 aluminum forged lowers, as older lowers made with 6061-T6 are weaker. And while most forged lowers will suffice or many people, billet lowers are stronger - but most folks are fine with forged lowers for average use, so save your $ and go forged.
Beyond that, some lowers do have features that others don't. That's why I always recommend the Aero Precision M4E1 lower.
On the M4E1, instead of roll pins it has a threaded bolt catch and a threaded takedown pin detent These make it easier to build (and R&R components) AND you can remove the buffer tube without having to worry about the detent and spring flying out. It has an
integrated trigger guard. It has a flared magazine well to make mag insertion easier. Finally, it has a nylon tipped tension screw that you used to adjust the fit between the upper and the lower (eliminate the wobble/play).
The Trigger: If you want accuracy out to 200 yards plus, you will want a nice trigger. I have opinions about which one(s) to use. I will share them with you if you like.
The best bang for your buck on a 2-stage trigger is the LaRue Tactical MBT-2S available in either straight or curved bow. No, it's certainly not a Geissele or Timney trigger, but it's 1/3 of the price of a Gisseele or Timney while packing great two-stage performance. They offer a single stage version as well if you're building a CQB/self-defense firearm, too.
The upper: This is where it happens. Do some research and pick your upper carefully. I see that Scoop doesn't like RRA, and that's OK. I have one that is easily the most repeatable I've ever shot.
I didn't say I didn't like RRA. I said they were overpriced. You can build a far better performing firearm for the same money you'll spend buying an RRA. For the record, I'm an RRA authorized dealer (but rarely order/sell from them) and, many moons ago, my first AR platform rifle was a RRA.
A 20" bull barrel will be super accurate but you will not want to carry it around.
For sure. At the other end of the spectrum, the thinner/lighter the barrel you get, the more prone it could be to warping if heated up too much (rare/never for the average shooter).
The bigger question is: what material the barrels is made of and who makes it. In the upper price range of a working man's AR, Ballistic Advantage, Aero Precision, Faxon and FN are my top choices, regardless of barrel profile.
Finally, barrel twist rate is important. Certain twist rates are better for certain projectile weights. A 1:7 twist rate means it takes 7" of barrel to rotate the projective 1 turn, while a 1:9 means it takes 9" to do the same. Be sure to do your research before purchasing a barrel, but understand there is no one single "best" twist rate. Generally speaking, the lighter the projectile, the more twist you want. Here's a quick chart to help see which rates work best for which weight projectiles for some very common 223/5.56 sizes:
The Optics: I can drop a Cayote at 100 yards with any of them (Red Dot, Iron or Crosshairs). But If you want to go out to 200 yards a good scope is required. Although I don't think you have to spend $1000 to get a good scope.
Lots of guys with decent eyesight are very accurate with iron sights well past 200 yards. But, yes, a nice magnifying scope is great for out past 150-200 yards. You're right, too -- no need to spend $1K to get a "good" scope. Lots of options below that.
IMO: if you are wanting to shoot prairie dogs at 200 yards you should look into an AR-10. There are more options for long range rounds. The uppers are more expensive however. You still could build something for under $1200.
The effective firing range of 5.56 NATO is upwards of 600 yards. No problem for smaller critters (e.g., prairie dogs) at those distances. But, going for bigger game at longer distances is best served by a bigger caliber (.eg., 308, 6.5 Creedmoor) off the AR10 platform. Sure, they can cost a bit more to build and shoot, but not crazy money more - just think of it as "super-sizing" your Big Mac meal ...